Designing Synchronous Counters Using JK Flip Flops

>> Good day, this is Jim Pytel from Columbia GorgeCommunity College.

This is digital electronics.

This lecture's entitledDesigning Synchronous Counters.

Okay, so in our previouslectures I've been giving you synchronous counters and we'vejust been performing an analysis of them.

And the question remains ishow do you actually make one of these things? So I mentioned previouslyit's kind an art form.

And what I'm intending thislecture to be is art school.

I'm going to give asystematic method to go ahead and design a synchronouscounter.

And we are going to beusing JK Flip Flops.

You can do the samething with D Flip Flops.

Takes a little bit more logicbut we're going to go ahead and use JK Flip Flopsfor these purposes.

When we created a 2 bit binaryup counter it was kind of one of those things where wecan see the transition.

In a state diagramfor a 2 bit binary up counter let's saywe're in state zero, zero, we're going upward out of 1, 2, 3, back to zero and so forth.

We can see that.

And we can visualize when doI want that MSB to change? Well it will togglewhen the LSB is 1.

Okay, if you think about thisyou can kind of see this, okay.

When do I want this toggle whenits previous state was high? What do I want this toggle likehere is 1, it's going to toggle to a zero when itsprevious state was high.

We can see that.

When do we want theLSB to toggle? Well all the timebecause I can see that.

It's, was a zero, goingto a 1, was a 1 going to a zero zero, 1 1 zero.

We can see that.

Not so easy all the time.

In our first example ofthis what we're going to do is design two bitgray code up counter.

First off start offwith a state diagram.

What is a two bit gray code upcounter state diagram look like? Chances are it lookssomething like this.

We are in state zerozero, go to zero 1.

We are in zero 1, we arein zero 1, go to 1 1.

Notice only 1 bitposition changes at a time.

That's the advantageof gray code.

And then let's countup, go to 1 0, count up, we recycled back to zero zero.

And we can do that samething with the truth table.

Present state, zero zero, goto zero 1, zero 1, go to 1 1.

And notice here I ampurposely not counting in gray code for the present.

I'm exhausting allbinary combinations.

So now what I'm doing, I'min 1 zero, where do I go? I go to zero zero.

I'm in 1 1, where do I go? One zero.

So again keep theorder for the present state in an exhaustivebinary combination.

And what I've kind of drawn hereis it's a synchronous counter that has a clock tied to it.

It's two stages obviouslybecause it's a 2 bit counter.

But what is the logic that wewant to put on those J&K inputs? And quite like our lastexample in an analysis of synchronous counters, those J's and K's don't haveto be tied together.

We're going to get independentlogical values for them.

How we do this isvery systematic means.

What we have to do isbasically start with an analysis of how a JK Flip Flop works.

If the present state is a zero and the next state istransitioning to a zero, i.


it's saying thesame, what could we have on our inputs for J & K? Well put it in memorystate, zero zero.

Okay, if its memory, youknow, we're going to be good.

However, what ifI was to reset it.

Well if it's already a zeroresetting it doesn't change it also.

So I could also potentiallyreset it.

So it sounds like a K inputdoesn't matter, doesn't matter.

It's going to be an X, right.

Let's look at that next stage.

If the present stateof that input is a zero and at the next clockpulse it transitions to a 1, what do I want to do? Well maybe I want to set it.

How do I set something? One zero.

Well ifa zero transitions to a 1 I could also toggle it.

So how do I toggle something? I'm actually going to go aheadand put a 1 on the K input.

So it sounds like that again, that K input doesn't matter.

Now let's go ahead andconsider a third case.

If we are a 1 and wetransition to a zero.

Well maybe I want to reset it.

Well also what about toggling? What if I toggled it? That would also makeit go to a zero.

So I could also potentiallytoggle the thing.

So it sounds like theJ input doesn't matter.

Now let's take that finalconsideration 1 going to a 1.

Yep, that's a memorystate, definitely memory.

Is that the only thingthat could happen? No.

What if I also setsomething that was already set, i.


put a 1 on the J? Sounds like the Jinput doesn't matter.

So what we've created here isa truth table that we can use when we reform theanalysis of this.

It's exactly whatI'm going to do.

I know in this case for designing synchronouscounters I know this state machine diagram.

Or from the requirements of thedevice I'm capable of figuring out the state machine diagram.

So I've got the presentstate and the next state.

What I have to do isfigure out the logic for the J & K Flip Flops.

Whereas previouswe had the analysis of synchronous counters.

The analysis of synchronouscounters we knew the present state, we knew the logicfor the J & K Flip Flops, we tried to figureout the next state.

So designing a synchronouscounters we've got that overarching generaldescription how we want the thing to behave or doing this, we are actually going to come up with the illogic forthe J & K Flip Flops.

This is how you do it.

You have the present state.

You have the next state.

Where do we get that from? We got it from thestate diagram.

Put them right nextto each other.

How many stages do you have? Well this is, excuse me, this is a [inaudible].

Its next state is dependentonly on its present state.

So there's no externalinput for this thing.

Anytime there's a clock pulseon this thing it's going to count in gray code.

I've got inputs forthe Q 1 stage and I've got inputsfor the Q zero stage.

And this is where ithelps to have like kind of those colored markers.

This is Q 1's present state.

It is transitioningto Q 1's next state where its inputs, it's these guys.

And do the same thingfor Q zero.

Okay, let's juststick a Q 1 right now.

Just divide these things upinto their own separate realms.

Okay, look at Q 1'spresent state.

It's presently a zero.

It's going to a zero.

Where are we on the truth table? Right there.

J could be a zero, Kcould be, don't care.

Okay, move on to the next one.

Q 1 is presently a zero.

It's moving to a zero, excuseme, it's moving to a 1.

Where are we? We're right herein our truth table.

So J could be 1, Kcould be, don't care.

Now move onto the third one.

We are a 1.

We're moving to a zero.

Where are we? Right here, okay.

So J could be don'tcare, K could be a 1.

Finally we are in aposition where Q 1 is a 1 and its next state for a 2 bit up gray code counter, it stays a 1.

So where are we onthe truth table? One is transition to a1, J, don't care, K zero.

What do we do with this stuff? Don't worry about it right now because we're only halfdone for the truth table.

We got to go ahead andfigure out for Q zero.

Because this is what I'msaying about using color codes or somehow organizing it.

Forget about Q 1.

Let's look at Q zero.

Q zero's present state is here.

It's transitioningto its next state on the positive clock edges.

What are its stages inputs? They're right there.

Look at it.

Was a zero, it's transitioningto a 1 right there, 1 X.

It was a 1, stayinga 1, where are we? Don't care, zero.

Next one, zero moving to a zeroright here on our truth table.

Zero X, not truth table, little cheat sheet.

Finally we are a1 going to a zero.

Should be don't care, 1.

So now what am I going todo with all these J 1, K 1, J zero, K zero inputs.

Well what I'm going to dois just to try to figure out the minimum SOPexpression for J 1.

The minimum SOP expression forK1, minimum SOP for J zero, minimum SOP for K zero.

How do I do that? Use the card on that.

So what I've got is fourpremade Karnaugh maps here.

And what I've got is Q 1 onthe left, Q zero on the right.

Again we've got 2bit input here.

If we add some externalinput we have to go ahead and count for that.

But in this caseit's a Moore machine.

It's next state ispresent only, excuse me, it's next state is onlydependent on its present state.

All you do is just take J 1, putin the, its appropriate K-map.

Come up with its[inaudible] SOP expression.

Do the same thing for K 1, do the same thing for J zero, do the same thing for K zero.

So let's go ahead andjust take the J 1 column.

Go ahead and putit in the K-map.

I see zero, 1, don'tcare, don't care.

What is the best expressionyou can come up with for J 1? Okay, what I see is rightthere, that's my best group.

Yes I could have justgrouped that upper 1 in the upper right hand corner.

However, if I'm makinguse of the don't cares, if they help me I'm not makinguse of them if they don't.

For example I would includedthis lower group of 2 because I've alreadyaccounted for that.

Okay, what is that? To me J 1's expressionlooks like it is Q zero.

So do the same thing for K 1.

What is K 1's populatedK-map look like? It looks like don'tcare, don't care, 1 zero.

Go ahead and find its group.

It looks like that so to me K1's expression should be not Q zero.

Now go ahead and populatethe K-map for J zero.

What we've got here is 1, don't care, zero, don't care.

What is its expression? We find that to bethe best group.

What is that representin the K-map? Looks like that, minimumSOP expression is not Q 1.

And we've come up with a minimumSOP expression for J zero.

Let's move on to K zero.

Take the K zero column, populate the K-map.

Don't care, zero, don't care, 1.

Go ahead and come up withthe best grouping for that.

What I find is is righthere, this group of 2.

Again I'm making use ofthose don't care situations if they help me.

I'm not making use ofthem if they don't.

That expression there is Q 1.

In a perfect worldwhat we've come up with here is the expressionsfor the individual J's and K's that will set, reset or stayat that particular stage at those positiveclock edges to go ahead and initiate a 2 bitgray code up counter.

The last step for all this.

The last step, check your work, go ahead and do an analysis of synchronous counter.

Implement the device, do theanalysis of synchronous counters and see if this thing reallydoes count up in gray code.

So let's go ahead andset it up for that.

So we've gone uphere is went ahead and implemented that device.

We're put that logicon those J and K's for their respective stages.

And again J 1 has Qzero, K 1 has not Q 1 and J zero has notQ 1, K zero has Q 1.

These are the resultantlogic that we came up with our designingportion of it.

We're going to goahead and check to see if this thing works.

How do we do an analysisof synchronous counters? What we do is wejust come up with J and K expressionsfor each stage.

Evaluate those inputs basedupon our present combination of inputs.

And then figure out the actions for those respectivestages, okay.

So what is J 1, K 1, values and actions givenpresent state zero, zero? Well J zero, excuse me, J 1 is always Q zero.

So I can go ahead andjust fill out that column.

What's K 1? What's not Q zero? So I can just say 1 zero 1 zero.

Our action, what is the actionbased off J 1 K 1 zero 1? It's reset, set, reset, set.

Go ahead and lookat the expressions for J zero and K zero.

J zero is not Q 1.

So I can just say 1 1zero zero, K zero's Q 1.

So what it's going to do isgoing to say zero zero 1 1.

What are the actionbased off those inputs? That is a set, a set, a reset, a reset.

Now what we're going to do isgo ahead and use those actions for those respectivecolumns and go ahead and figure out our next state.

And if everythingworks out correctly, you know what it should do? It should do this.

That is our 2 bitgray code up counter.

So what we're going to dois just check our work, do our logic work.

So this section heredeals with a transition of this present stateto this next state.

Okay, go ahead andso that analysis.

If it is a zero it'sbeing reset to a zero.

If it is a zero, it'sbeing set to a 1.

If it is a 1, it'sbeing reset to zero.

If it is a 1, it'sbeing set to a 1.

Go ahead and do that sameanalysis for the Q zero inputs.

Where are the Q zero inputs? Right there.

That action is affectingthis present state and it's changing itto that next state.

So if it was a zero, it's being set to a 1.

It was a 1, it'sbeing set to a 1.

If it was a zero, it'sbeing reset to a zero.

If it was a 1, it'sbeing reset to a zero.

Go ahead, does our resultantfinite state machine do what it's supposed to? Okay, our designimplements zero zero, it goes to zero 1, looking good.

It is zero 1, it goesto 1 1, looking good.

It is 1 zero, it'sgoing to zero zero.

That's that transition rightthere, we're looking good.

Finally our last state, 11 where's it go to next? One zero.

Oh my gosh, our design worked.

So systematic, again systematic, that's the way yougo ahead and do that.

Take the present state, compare it to the next and use that cheat sheet right here.

You have to know how thesethings work given a present state and you know its nextstate, go ahead and figure out those J & K inputs.

Again just take those individualJ & K inputs and put them into their own individualK-maps and come up with a minimum SOPexpressions for it.

So that was a Mooremachine example.

Again how was Moore machine? Its next state is onlydependent on its present state.

What if I had an externalinput that I wanted to go ahead and have different modes formy finite state [inaudible]? So let's go aheadand do an example of designing a synchronouscounter that is a Mealy machine which next state is dependentnot only on its present state but also some external input.

Okay, so our second example of designing synchronouscounters using JK Flip Flops is [inaudible] the example.

It's a finite statemachine external inputs.

And the student among you mayrealize that this state diagram which I've drawn righthere is the exact same one for the example thatended the analysis of synchronous counters.

So ideally what'sgoing to happen here is when we design this we shouldget a fully minimized SOP expressions for those J& K inputs for each stage which exactly matchesthe analysis of synchronous counters example.

Again look at thisstate diagram here.

What it represents isa zero zero start state when X is zero, it goes to 1 1.

So it's an external input.

When X is 1, it goes to zero 1.

So those are two choices.

There are two, excuse me, there's a single choice but there are two exits.

You either go X iszero 1 and you're going to go two different directions.

If it's zero it's going tokeep on going in this direction and keep on goingin that direction.

That zero zero isjust a feed in state.

Whereas if it was in 1, ifX was 1, we are at zero 1, 1 zero, 1 1, back to zero 1.

If at a time howeverwe switch modes, let's say for example we are instate zero 1, we are in mode 1.

We would go to 2 but themode suddenly switches to X equals zerowhere would we go? We'd go back to 1.

So using the state machinediagram, let's go ahead and figure out what ourpresent state of inputs are? And when I say inputs, again it's present state and the external input.

So there is how manyinputs here? So there's two stagesfor the present states.

Q 1 and Q zero andan external input.

So there's three inputs.

How many possible combinations? It sounds like there's eightpossible combinations for this.

And then just go ahead and basedoff of those present states and external inputsthere, go ahead and figure out what the next state is.

So what I've drawn hereis a bare truth table.

I'm setting you guysup for this already.

And this is again, this is kindof what I'm expecting you guys to have an understandingof this.

Is just, this is systematic.

And again this is art school.

I'm giving you the stepsto go ahead and do this.

What do we do every single time? Just look at the state diagram.

Here's out inputs.

We are in present state zerozero, we are in mode zero.

What's our next state? It sounds to me likewe'd moving to 1 1.

Okay, we are in present statezero 1, our mode is zero, X is zero, where do we go to? It's X state is also 1 1.

Okay, how am I doing this? I'm just looking fromthe state diagram.

Our first one we wentfrom zero zero to 1 1.

Now we are in zero 1.

We're going to 1 1.

Let's go ahead and if youcan, see if you can figure out the next state, i.


the output for based off that state diagram see ifyou can go ahead and figure out the next Q 1and Q zero state.

So hopefully your next stateoutput looks the same as mine.

And again let's justpick an example here.

Okay, we are currentlyin present state 1 zero, however, we are in mode 1.

Where are we? We're right there.

We're in mode 1.

Where do we go to? One one.

Okay, so justreading that state diagram and putting it into this table.

All right now, what do we do? We divide these thingsup to each stages inputs.

J 1, K 1.

It is looking atthat one's present state and it's transitioningto this next state.

So it was a zero, it goes to a 1.

Where are we? It's right there.

So what we do is just fill outthese columns, 1, don't care, finally the, this nextone here, what is it? We are in a zero, we are going to a 1, so we're in the same spot.

One, don't care.

And let's go ahead and seeif you can compare each one of those present states of Q 1'sand the next states of Q 1's.

And use this truthtable which we've, the little cheat sheet truthtable there to go ahead and figure out for the J and K and hopefully yoursshould look like this.

Okay, so those areJ 1, K1 values.

Now just go ahead and whatare we going to do now is look at Q zero's present state.

It's transitioning toQ zero's next state.

What does it affect? What are its inputs, excuseme, it's J zero, K zero.

So it presently inzero, moving to a 1.

Where are we? It's 1, don't care.

Now we are 1 moving to a 1.

Where are we? Don't care, zero.

Go ahead and see if youcan fill out the rest of the J zero, K zero column.

And there we go, hopefully the J zero and K zero's look very similar.

Now what's our next step? We're going to go aheadand put J 1 into a K-map and develop the minimum SOPlogic expression for it.

Do the same thing for K 1.

Do the same thing for J zero.

Do the same thing for K zero.

And the key thing is is justonly do the expression for J 1.

Don't try to combine J 1with J zero or K 1, K zero.

So it's entirely separate.

So let's just look at J 1.

Just go ahead and try tofill out the K-map for J 1.

And if you need help withK-maps just go back and it's in the K-map lectures.

Should be prettyfamiliar to you.

It's 1 1, don't care, don't care, zero 1, notice the gray code there, don't care, don't care.

How do I develop theSOP expression for J 1? Again groups of 1, 2, 4, 8, 16, 32, so on and so forth.

Use the don't caresif they help you.

Don't use them if they don't.

So here's my firstgroup right there.

It's a group [inaudible].

That looks like that is Q zero.

My second group I'm going tograb a group of four also.

What is that? That looks like not X.

Somy final SOP expression for J 1 is Q zeroor not external.

Okay, and if you rememberright from our previous example of analysis synchronous countersthat's the original input I gave.

So we're tracking here.

Go ahead and see if youcan populate K 1 map, populate a J zero map andpopulate the K zero map.

Just do the populationright now.

So hopefully we'llstart off the same spot.

So there is the populationof those individual K-maps.

And let's look atK 1's expression.

So come up for the minimumSOP expression for K 1.

But I'm going togo ahead do those, I'm going to grab this groupof two right here and I'm going to grab this groupof two right there.

Okay, so the group inblue, what is that? That is not X and not Q zero.

What's the group in red? The group in red isQ zero and X.

Okay so the final SOP expressionfor K 1 is not X and not Q zero or Q zero and X.

Okay, J zero's expression.

J zero's expressionis pretty neat here.

Look at it.

Okay, we've got acolumn of 1's all the way down in the not Q zero column.

But look it, we've alsogot X's, i.


don't cares in that Q zero column.

So what would you do? If it doesn't matterif it's a zero or a 1 for the Q zero column, just goahead and group the whole thing, okay it's a group of eight.

What is a group of eight? Basically it's alwaysgoing to be a 1.

Okay, so J zero isalways going to be a 1.

Let's go ahead andlook at Q zero.

What I'm going to do is finda group of two right there, another group of two there.

What do I get here? So this first one is going benot X, end Q 1 or X and not Q 1, excuse me, X and not Q 1.

So what we can do is takethe final SOP expressions for those J 1, J 1, J zero, K zero inputs for each stage.

And go ahead and implement it.

And what we came here with thisexactly what we had originally had in that, the endexample of the analysis of synchronous counters.

When we figured out thestate machine diagram for this one actually doesimplement with all what we're, what we've designed here.

So again I can always go back and check my work using whatI developed for the J zero, K zero, J 1, K 1 stages.

And go ahead and see how thisworks using that tabs or method for analysis of synchronouscounters.

So let's go ahead andclose up this lecture with a couple things that youmight be able to tackle here.

Just here's somesuggested exercise.

And I'm not going to giveyou the state diagram for these things whereaspreviously I had given you guys the state diagram.

I'm going to go ahead andhave you design it from there.

I'm actually just going to giveyou guys a verbal description of these things.

It says one of thosesteps here you've got to take this leaps of logic.

What does the state diagram for these two suggestedexercises look for? So for the first one herethink about a 2 bit binary or gray code up counter.

So it's got an externalmode, okay, that's called B, let's call it B slashnot G.

Okay so that's an external input.

When that B slash not G is1 it's counting in binary.

When B slash not G is in zero, its counter in 2 bit gray code.

So there is an external input inaddition to its present state.

How would it look inthe state diagram? And let's say it switches mode.

Okay so it was inbinary mode and it is in a certain present state.

And it suddenly switchesto gray mode.

Where would it go? Out, so you go to its nextgray code sequence based on that present input.

So this is pretty neat.

These conceptual exercisesactually visualize how these things work in a state machinediagram before you even do any of these techniques that we'vedone in this lecture here.

The next suggested exercise, this is a good one here.

See if you can design a 3bit odd even up counter.

So we've got oneinput, odd slash even.

So let's go ahead and sayit's an external input.

There's that external input.

That's making a decisionwhere it goes.

So let's go ahead and say whenit's in zero, go to even mode.

When it's in 1, go to odd mode.

And by the way so you don'thave to use this clunky notation for these external inputs, you can call it X or EX or E or whatever you want to do.

I just don't call it E forthat particular exercise.

Just come up withsomething memorable.

You don't have to usethis clunky notations.

But think about this 3bit odd even up counter.

If it's in odd mode, it'sgoing to obviously go to the next odd numberhighest in the sequence.

So for example 1 goes to3 goes to 5 and so on.

If it's in even mode, it's going to go from 2 to 4 to 6 and so on.

But what happens if it's ineven mode and an even number? Let's say 4 and it suddenlyswitches to odd mode prior to the next clock sequence, getting that clock edge.

What would it do? Well it would go up tothe next odd number.

So see if you can up withthe state machine diagrams for these things.

These are excellent exercisesto practice what we've learned in this lecture designsynchronous counters using JK Flip Flops.

Okay, let's go ahead and seeif we can in our next series of lectures here go ahead anddescribe some counters used in some different technology.


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at the wheel and this is gonna follow your natural foots motion it's gonna it's economically correct it's gonna give you that cushioning in the arch we have as I mentioned the impact pillow so you're getting that extra cushioning but it is a it is a flip flop so

it's meant to be super lightweight and flexible its packable of these throw it in your bag take it to the beach where I like that these can get wet you know cuz there are places like if you go to the gym a lot or you go to the

spas and you do the saunas I hate to walk in barefoot to those places great or if even you know hey sometimes you're looking for an affordable like hotel if you go on vacation and you have a huge family and you're trying to keep the cost low yeah

you know you'll walk in and you'll be like not the quality I expected so that's the one I'm wearing the shoes on the carpet I'm wearing the shoes into the shower you know this is speaking to your point a great packable vacation shoe this is I mean really

feather-light you know you almost feel the support the way this shoe under your foot you know am I gonna be jogging doing exercise and probably not but you know you feel that it gives you more than an ordinary flip-flop and so I hope you try these out today

sixteen dollars on a credit card free shipping they're so cute to know I really just leave by the door I mean you mentioned you're not you're not gonna be out jogging in no but maybe when you get back from jogging and you take off your trainers what do

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for a walk after work or if I'm going for a stroll at lunch they're as comfortable as the rest of our sandals had a really great price with a really fun print less height on this one a lot of times the sandals have a little more than an

inch this one is literally a one inch flat molded unit so it's almost like a little bit thicker or it's like what you wish your favorite pancake was like just a little fat it's got just that a little bit to give out the cushioning so that you don't

have the foot fatigue at the end of the day or the knee fatigue or the back fatigue leads into the other brand Stephanie right is about pressure defusing the whole technology proposition is about is about pressure diffusion and everything that we've seen so far today has that Evie

a midsole so hits the lightweight very flexible great flex cruise and it's all a PMA approved that's oh that's a wonderful seal of approval to have across the board whether you're going for the triple density the single density you know and the eye cushion you have those impact

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day I save the turtle Jared instead of falling on my hand if I had an impact pillow zero eight seven five oh eight is your fit flop flip flop yeah I did it 69

Designing Synchronous Counters Using D Flip Flops

>> Good day.

This is Jim Pytel from ColumbiaGorge Community College.

This is Digital Electronics.

This lecture is entitledDesigning Synchronous Counters using D Flip Flops.

So we went over in ourprevious lecture how to design a synchronouscounter that could count in whatever sequence wewanted to use JK Flip Flops.

Okay, the little secretis I actually kind of showed you guysthe hard way first, and in comparison this DFlip Flop method is going to be substantially easier.

We're even going to usethe same two examples here to illustrate you canuse different technology to design a finitestate machine.

This first example was, again, our two-byte graycode up counter.

There's no external inputs, it's just more machine.

Its next state is dependentupon its present state only.

So we've got our present input, we can determine our next state.

And what I've drawn here on thebottom is D Flip Flops, okay? There's only one input, whereas, a JK Flip Flop has two inputs and four different modes, what's D Flip Flop do? Well, the value Q isbasically sampling D at those positive clockage[Assumed Spelling].

What we have to do is justmake D, the input D equivalent to what we want tothat next stage to be, and you can reallysimplify this is what is that next state input there? Well, that's D, we want our nextstate, our ideal next state.

Say, for example, right here, we're looking in this column, Q1, what do we wantthe input for D1 to be? Oh, we want it to bethis one right here, at that next positiveclockage we want it to be Q1, at the next positive edge, 4Q0, we want D0 to be that, so it's very simple.

All we're going to do is makeour K maps for D1 and D0, basically, Q1 is D1, that'sthe input for stage Q1.

What is the input for stage Q0? Well, it's D0, wewant those values.

What we're going to do is we'regoing to take D1, go ahead and populate our K maps, take D0 populate our K maps, and you should come up withsomething like this, okay? So we've populated the Kmaps for each stage's inputs, and now what I cando is just go ahead and take the minimumSOP expressions for each of the stage's inputs, determinethe minimum SOP expression for each stage inputs.

What I've resulted withis D1 is Q0, D0 is not Q1.

We'll go ahead and nextstep we're going to go ahead and implement the designand then what we're going to do we're goingto test it, okay? So look at our implementationthere, D0 is being fed, not Q1, and D1 is being fed Q0.

So let's go ahead and try atiming diagram analysis of this, and what we've gotis right here.

I've redrawn theimplemented circuit here.

So, first, let's go ahead andassume that we are in state 00, and again we are at2 byte gray code, let me just redraw the statediagram real quick just to make sure that we areimplementing exactly what we want to.

In a perfect world we are instate 00, we will transition to 01, then from there to 11, from there to 10, and back to 00.

So what I've drawn is theoutput stages, Q1 and Q0, but additionallyI've drawn not Q1, so we can do ourtiming diagram analysis.

First positive edge comesalong, what is the state of D0? Well, it's not Q1, which is currently a 1, at that positive edge Q0suddenly becomes 1 and, again, there's a slightdelay right there.

What is the input for stage Q1? Well, it's Q0, Q0 atthat positive edge if I remember right was a 0, sowhat does Q1 do, it stays a 0 and not Q1, obviously staying 1.

So what we did we went from 00up to 01, just like we expected in our timing diagram, so let's go ahead and see if we move to stage 11 now.

The next positive edge comesalong, sample Q0 is right there, samples not Q1 right there, D0'sinput is not Q1, so it's going to stay a 1, and now whatis the input for stage Q1? Well, it's D1, which is Q0, it's a 1 so what happens hereis Q1 is going to go up to 1.

We've made that transitionto, as we'd expect, 11.

What does not Q1 do? It goes back down to 0.

Go ahead and do the next input.

Obviously, we should hopethat we're going to go to 1, 0 and at that positive edge theD0 input is a 0, so that goes 2, 0 and then the D1 input atthat positive edge is a 1, so it's going to stay a 1.

We've made that transitionto 1, 0 as we'd expect for a gray code counter.

Next positive edge comes along, the D1 input is a 0, the D0 input is a 0.

Where have we gone? We've gone to 00 as we'd expect for our 2 byte graycode up counter.

So if you do these timingdiagrams over you see that entire sequence, 00, 01, 1, 0 – 1, 1 – all the way down to 1, 0 andwe're starting back again at 00.

So there's an alternativemethod to doing this and it's substantially easierthan using the JK Flip Flops.

So let's go ahead anduse what we've done here, using D Flip Flops.

I'll just do that sameexample that we did for design and synchronous countersusing JK Flip Flops.

So our next example of designingsynchronous counters using D Flip Flops is a finitestate machine that is actually a kneeling[Assumed Spelling] machine where its next stateis dependent not only on its present state, but some external input.

And if you're looking at the state machine diagramyou'll recognize this same one I did in the analysis ofsynchronous counters and the same one I did designingsynchronous counters using JK Flip Flops.

What I'm trying todo is show you that you could potentiallyimplement this same counter using a different technology, in this particular case a DFlip Flop and using D Flip Flops to design a synchronous counter like this is substantiallyeasier than JK Flip Flops because, again, there's only one input.

And what is the input Dfor each particular stage? What it should be, itshould be the next state.

So all we're going to do isjust take that next state and make that our D input.

What we did is we readour state machine diagram, determined our present stateand the external input, determine the next state, what is the D inputs.

Well, it is the next state.

What we could do is takethose D inputs and put those into individual canops[Assumed Spelling], so basically D1 isgoing into the D1 canop, D0 is going to the D0 canop.

Go ahead and evaluate thoseindividual expressions.

What I came up with for theD1 expression is X and Q1 and not Q0, or notX and Q0, or not X and not Q1, or not Q1 and Q0.

The D0 expression, we've gota big old group of four there, and it's not Q0, not X and not Q1, or X and Q.

So now whatI can do is go ahead and implement thisdesign and test it, and using a timingdiagram is going to be a little bitcomplicated for this.

We're actually goingto go ahead and kind of use a tabular analysis ofthis, to go ahead and see, okay, here are our D inputs, hereis the synchronous counter with the following D inputs.

And what I've done I've drawnour SOP expressions for D1 and D0, and notice here, too, D1 is matching this right here, D0 is matching this, so there's a little bit of a Flip Flop there, justgot to again stay organized.

And based on those input stateshere are our inputs right here, evaluate each one of thoseintermediate expressions for D1, based off those present inputsthere evaluate the intermediate stages for D0, based upon thoseintermediate stages evaluate D1 and D0.

What's the next state? Well, it is D1, D0.

So let's go ahead, at leastfor the D1 column, go ahead and evaluate thoseintermediate expressions for D1 and you should looksomething like this.

So the intermediate productterms for D1, let's go ahead and figure out what the or ofall those product terms are, it should look somethinglike this.

Now go ahead anddo this same thing for D0's intermediateexpressions, determine those values.

So based off those intermediateproduct terms evaluate D0, it should look something likethis, and there we have it.

What is the next stateQ1, Q0, the next time that positive edge comes on? Well, it's D inputs, D1and D0, so we can go ahead and just translate D1 and D0over to that next Q1, Q0 column.

It should look somethinglike this, and now go ahead and see does that present stateof 00 in mode 0, does it go – well, where does it go? It goes to 1, 1 – so anX is 0, it goes that way.

We are in present state 01mode 0, where do we go to, also to 1, 1 when X is 0.

What I'm doing is constructing, reconstructing this statediagram based on an analysis of what we came up with from thedesign and see does it, in fact, institute the state machinediagram which we're into, and you'll find as you gothrough these present states, next states for each mode because again this is modeX equals 0 and mode 1, it does in fact implement thedesired finite state machine.

Again, designingsynchronous counters, you can use JK FlipFlops or D Flip Flops, D Flip Flops are substantiallyeasier because, again, there's only one input there.

And we've designed a synchronouscounter using a JK Flip Flop, we've designed a synchronouscounter using D Flip Flops.

Let's go ahead and see howcounters work in VH DL.

Before we move onto thenext lecture, though, remember the two exercisesthat I gave you at the end of designing synchronouscounters using JK Flip Flops, the two binary/gray up counter and then the 3-byteeven-odd counter.

You might want to take a lookat those two suggested designs to go ahead and see if you canimplement those designs using D Flip Flops.


The Kind of Love You Need | Sandals Church

– My non-negotiables wereyou have to be at church and you have to know Jesus, you have to be able to love dogs as well.

– There were things that Ididn't care as much about, because, hey, he's cute.

(upbeat music) – So they have to like want a family or at least want one or two kids.

– Honestly, if they'rea Dallas Cowboys fan, it's just not gonna work.

No, in all reality, the good question just in looking at thislist is, am I this? Do I have good community? Am I invested in a local church? Am I making financial wise decisions? Am I rooted in Christ? (upbeat music) – Good morning Sandals Church.

(congregation clapping) Good morning.

Thank you to all those families who are helping grow Sandals Church.

Yeah, man, it's fun to, it'sfun to grow your family.

It's hard to raise a family, amen? Had to be really carefulwhat I was gonna say there.

(congregation laughing) Hey, we're in a seriescalled “Non-negotiables”, it's a series about love.

Look, if you're a young person, lemme ask you a question, do you have a list? Do you have a list ofwhat's non-negotiable? Have you ever sat down andsaid, “What am I willing “to accept when it comes to love? “What am I not willing to accept?” What is something that ifa guy says this, I go no, absolutely not? What if, guys, and know guys have a list, it's just, she's hot, that's it.

Then everything else isa big blur after that, you need to have a list.

Listen to me guys, the devil's beautiful, and you might marry her.

(congregation laughing) Same is true for you gals.

Look, if you're single, you haven't screwed upyet, you don't have to.

If you're divorced, youdon't have to do it again, you can learn, right? You can learn.

God has a list of non-negotiables, and in this series it's aboutfinding the love you need.

You know what most of our problems is? Is we're looking for the love we want.

And we're not lookingfor the love we need.

God knows what you wantand He knows what you need.

And He's gonna teach you tolook after a kind of love that you need, so that youcan have the life you want.

This is the firstnon-negotiable in this series.

I think every one's gonna blow your mind.

I'm guessing this isn't on anyone's list, but you're wrong, God's right, this is the most importantquality when it comes to love, and this needs to be on everybody's list.

Write it down, I needa love that can listen.

Married people, you ever felt unheard? You ever felt unheard? Come on, ladies, it can't justbe a guy given me an amen.

(congregation laughing) You ever felt unheard, ladies? You ever felt ignored? You ever felt missed? You know why that is? We don't teach our men to listen.

– [Congregant] Amen.

(congregation laughing) – Ladies, you're not muchbetter, but you are better.

We need a love that can listen.

Proverbs 31 is a chapter on love.

A lot of you women have beentold the Bible's written by men, it's all about men, it's trying to maintaina patriarchal society.

Listen, a lot of theBible is written by men.

This chapter is written bya woman, how do you know? She tells us.

Listen, my son, listen, son of my womb.

Contrary to current thinking, men don't have wombs.

(congregation laughing) Just women have wombs, justwomen give birth to kids.

Lemme tell you something, women have a deeper connection with their children, becausethey grow inside them and they are connected to them.

When my wife and I go on vacation, day three, she wants to talk to our kids.

Listen to me, day three, I forgot we have kids.

(congregation laughing) She says, “Do you wanna talk to your son?” I'm like, “No, that'swhy we're on vacation.

” (congregation laughing) She wants to check in, she loves them, she cares for them.

She says, “Listen my son, listen my son.

” Why does she say it twice? Is any woman in here raising a boy? They don't even hear thefirst time, amen moms? This is how it sounds in the Hebrew, (speaks in foreign language), and it's actually, “What, son, what?” Which means listen, before I make you listen.

Listen, my son, listen my son, son of my womb, listen my son.

Ah, this is so sweet, the answer to my prayers.

Isn't it amazing howmothers love their sons? I have to remind my wife, “Hey, I'm number one.

“Hey, hey.

” They love their boys.

Don't spend your strength on women, why? Women understand women.

Listen to me, guys, yougotta listen to women, 'cause they can sniff outthe devil before you can.

They know, I don't like her.

You're like, “Why?” I just know.

(congregation laughing) Do not spend your strength on women, nor your vigor on thosewho, circle this word, ruin kings.

I don't care how talented you are, or how talented you think you are, or how much your mama loves you, your love life can screw up your life.

And it happens all over the world today.

People following theirhearts invite destruction.

I need a love that can listen.

We talked about last week, and if you missed last week, go back to it and I explain these Greek words more thoroughly, but the Greeks had four ideas for love.

Many languages and manycultures have different words for love.

In English, we got one word, I love you, I love pizza.

And sometimes you findout they love pizza more than they loved you.

But the Greeks had four words for love and the first word is eros.

Eros is a romantic sexual love, and here's the problem with eros, you need a love that can listen, eros doesn't listen to anyone.

It is blind, right? You ever heard that, love is blind? It's also deaf, it doesn't listen, it doesn't listen, it is so powerful, it is so strong, andmany people fall in love with a person they findout they don't like.

And you say stupid things, “We have so much in common.

” Like what? We like vacation.

We like walks on the beach.

We like sips of wine.

Who doesn't? So do serial killers.

Right? And we just say stupid things.

Love makes you blind when it's eros, it literally lowers your IQ, whatever it is, it drops.

– [Congregant] Amen.

– And you just like, “I love you.

” It doesn't listen, itdoesn't listen to friends, it doesn't listen to family.

It doesn't listen to God.

We're in love, we're gonna get married.

You don't even have a job.

We're gonna live on love.

(congregation laughing) Okay, that's gonna last eight minutes.

Then what are you gonna do? Listen, if you're a young person, you can learn nothing fromsomeone who's fallen in love, but you can learn a lot fromsomeone who's stayed in love.

You can learn nothing fromyour friends on Facebook, find an old couple in our church that can barely walk, butthey've been together, that's love, that's love.

You see, real love outlasts eros.

It does.

This week, or excuse me, last weekend was Valentine's weekend, my grandmother went andmet with my grandfather.

They don't live together anymore.

He doesn't know who she is, he doesn't know who I am, but she went to him on Valentine's Day and I have a pictureof them holding hands, and he's smiling.

They've been married 75 years, they know what love is.

Eros is long gone, butlove is still alive, love is still alive.

Listen to me, young people, that's what you want.

That's a love story.

Storge love, right? It's powerful, it's strong, it's what the mother has for her son.

Listen, my son, listen to my son.

Listen, son of my womb, son of my prayers, storge love listens to parents and family.

You gotta learn to listento your family members, you gotta learn to listen to your dad, you gotta learn to listen to your mom.

Listen to me, one of thereasons I am doing this series is 'cause I have two daughterswho are ready to date and get married.

And listen to me, guys, I'mconcerned, not about them.

(congregation laughing) I'm concerned about you guys.

And I told my daughters, you cannot date a guy unless he asks me.

You gotta see theseguys, (fearful moaning).

I'm like, “You're notasking me to marry you, “you're just asking to takemy daughter out on a date.

” They're terrified.

And I told my daughters, “If he can't face me, “he can't lead you.

” And listen to me, ladies, ifhe is not a husband category, why are you dating him, whyare you wasting your time? Some of you need to dump that chump, amen? (congregation laughing) I mean, not now in service.

(congregation laughing) There's Phileo love.

Phileo love is friendship, right? These are your friends.

If you start datingsomebody, and they tell you that you can't have any friends, that's a jealous love, that's a dangerous love.

Phileo love listens to friends.

Hey, man, I'm concerned.

Hey, man, I'm worried.

But agape love, agape love listens to God.

There's a higher love, there's a different love, it's stronger than eros, itlasts longer then storge, and it's deeper thanphileo, it listens to God.

Here's why listening is a non-negotiable, love must listen because love is learned.

You don't fall in love, you learn how to love.

This is why nobody stays in love.

This is why we're allfascinated with “The Bachelor” or “The Bachelorette”, which is the, just the worst idea ever.

When they fight about who'shere for the right reasons? I'm here for the right reasons.

I don't think she's here for the, I don't think anyone ishere for the right reasons.

(congregation laughing) Love must listen because love is learned.

Proverbs 26, many claims, underline that, many, many claim to have unfailing love, but a faithful person who can find? Why do we let Hollywoodtell us what love is? They're not good at it.

They're not good at it.

Tammy and I went to a movie this week, I told her, I said, “I'm fairlycertain Hollywood hates us.

” You notice how theytake a beautiful movie, it's wonderful, it couldhave an incredible ending and they want you to leave miserable.

What's wrong with them? Maybe they don't know about love.

The Book of Proverbs says many claim to have an unfailing love, oh, but a faithful person who can find? Do you know what that means? True love is faithful, true love lasts, true love goes to a nursing home when your husband doesn'teven know who you are.

– [Congregant] Amen.

– That's true love.

The Book of Proverbs has 31 chapters, 36 times it mentions love.

This is how the Book of Proverbs begins, it ended with a mother talking to her son, it begins in chapter onewith a father talking to his son.

It begins this way, “Oh, my son, listen to me, “listen to me, don't hate my correction.

“Don't forsake your mother's instruction.

” And it ends in Proverbs 31 with, “Oh, son, “son of my womb, son ofmy prayers, listen to me.

” You see, some of you are fooled and you think love is for the young only.

Listen to me, it's the old and experienced who know what love is, andthat's who you need to listen to.

Love must listen because love is learned.

And we're told, “Oh, you'll know when you know.

” “Oh, you'll just fall into love.

” No, you're gonna fall in a hole, that's what you're gonna fall in.

Love must listen because love is learned, write this down, love must be taught.

You gotta teach people howto love, you gotta show 'em.

You gotta instruct 'em.

That's why it's so important, we just did a family dedication, you need to bring your kids here so we can teach them how to love.

And they need to learnhow to love from God.

Because God is love, and the Bible says this is what love is, it's not that you loved, it's that God loved us andHe shared that with us.

Love must be taught.

Titus 2:4, these older women, and you can pray about itif this is you, ladies, I'm not gonna point it out, but I'm gonna say ifyou ask, “Is that me?” It probably is.

Like if you question it, it's you.

(congregation laughing) these older women musttrain the younger women, ooh, this is interesting, older women must train the younger women to love their husbands.

– [Congregant] Amen.

– And if you question that, ladies, it's because you're single.

– [Congregant] Amen.

– You will love the guyuntil you marry him.

And then you'll be like, “Things need to change.

” (congregation laughing) The older women musttrain the younger women to love their husbands, and their children, what? You know why? You don't have 'em.

There's a reason God makes children cute, so we don't kill them.

(congregation laughing) Tammy and I went out on a date, no kids, it's wonderful, it's wonderful, no kids.

And there's a couple, they met together and they got their kid andtheir child has just learned it has a voice.

All through dinner it'sdoing this, 'Ah, ah.

” And that's cute twice.

And then the third timeyou're like, “Slay the child.

” (congregation laughing) Their whole dinner, the kidis like a dolphin, screaming.

It's summoning whalesin the Pacific Ocean.

It's horrible, they can't even eat.

It's going to shatter glass.

Listen to me, if you havechildren under five, I love you, but you're on the threshold of hell.

(congregation laughing) Every single day is a battle.

If you're here at church, praise God, you survived.

It's true, isn't it, parents? Every single day you pleadwith your children not to try to die, that'stheir mission every day.

(congregation laughing) I must die today, father.

And parents have to commit together to try to prevent their death, and they're mad at you when you intervene.

Right, they try to puttheir finger in the socket, and you say, “No, ” and they're like, “Oh, you're a terrible parent.

” (congregation laughing) And there's part of youthat's like, “Well, try it.

” (congregation laughing) These older women musttrain the younger women to love their husbands.

You know what, love is hard.

Love is challenging.

I don't even like beingwith myself all day, much less another person.

You get married and you're like, “Wow, you're gonna be around.

” (congregation laughing) I mean, when you have siblings, sometimes you get your own rooms.

In marriage, that's not true.

Tammy and I share a room.

She has her closet, and we have mine.

(congregation laughing) I'm always having to make roomfor her stuff in my closet.

(congregation laughing) The builders should changeit, it's not his and hers, it's hers and theirs.

The older women musttrain the younger women to love their husbands and their children.

Some of you, you don't evenrealize why you go to church.

Some of you didn't evenwanna go to church today, but you're here.

Here's why you need to go to church, because you need to learn how to love.

And the world won't teach you, the world will not teach you, the world will teach youwhat you want to hear, they will not teach youwhat you need to hear.

Here's what Paul says to ayoung pastor named Timothy, he says, “The purpose of my instruction.

” This guy wrote half ofthe Christian Bible, he wrote half.

He's way smarter than you, he's probably thesmartest Christian, ever.

You say, “Why do youknow that, Pastor Matt?” Because God asked him towrite half the New Testament, and He didn't ask you.

– [Congregant] Amen.

– He says the purpose of my instruction, this is the guy who wrotehalf your Christian Bible, here's why he's writing, here'swhy he writes these letters, here's why he has theseteachings, these sayings, here's why he wants us to meet, to gather, to be in community group, to worship, here's the point, the purpose of my instruction is that all believers would be filled.

I want you to circle that word.

Do you know why you need to be filled? Because you're empty.

Every single week you run out of love.

Every single week you run out of love for people you swore youwould never not love, you run out of love.

You run out of love for your husband, your wife, your kids, your family, your friends.

Sometimes you run out of love for me, you're like, “Oh, just wrap it up.

” (congregation laughing) The purpose of my instructionis that all believers, that's you, would be filled with love.

Not love that comes from eros, not love that comes from storge, not love that comes from phileo, but agape love thatcomes from a pure heart.

God is the one person in the universe that never wants to use you, He wants to deliver you.

It comes from a pure heartwith a clear conscience.

You see, God's love doesn'tjust change your heart, it forgives your sins.

Some of you are so heavy, so broken, so overwhelmed with sin, and Jesus is begging youto let Him take that away.

But God only cleanses what we confess.

If you won't share it, Jesus won't heal it.

That all believers wouldbe filled with a love that comes from a pureheart, a clear conscience and a genuine faith.

Not everybody that claims tobe a Christian is a Christian.

Even people that areon christianmingle.


(congregation laughing) the Bible says love is patient, and love is kind.

That's the first sentence.

You know what the first sentence about God's love teaches me? I have a lot to learn.

I'm impatient every day.

I lose my mind on a regularbasis waiting for my wife.

She's always concerned I'm gonna be late.

It's like, “Come on, babe, let's go.

” Look at the next word, loveis patient and love is kind.

Anybody raising childrenthat were just born kind? My kids were born biters, does anybody have a biter? Tammy and I had to go to preschool, we were called into a meeting at preschool and here's what they said, “Ifyour child continues to bite, “we will not allow yourchild in preschool.

” My kids were biters.

One day after church Igot called into the back, into Children's Ministry, thisis we need to talk to you.

And I said, “What happened?” “Your son bit someone.

” Can you imagine you come to church for the first time andyou bring your child, and you dress them up, (congregation laughing) they're so cute and you put'em in Children's Ministry and they're attacked by a dinosaur? And then they ask you, “Oh, it must have been somebody “who came to church for the first time “and they hadn't raisedtheir child to be loving.

” No, no, it was the pastor's son.

(congregation laughing) He brutally attacked our child.

(congregation laughing) I never sat my kids down and said, “This is how you bite another child.

” (congregation laughing) You see, you don't teachchildren to be selfish, you don't teach children to be violent, you don't take your kidto the playground and say, “Now you run and shove that girl.

” They just do it.

You don't teach your daughters, “This is how you gossip “about another girl onInstagram so she cries “and never wants to go to school again.

” But they do it.

Love is patient, love itkind, love is not jealous.

Love is not boastful.

Some of you are already out.

Strike one, strike two, you're out.

It's not proud or rude.

Those are the things I'm good at.

It doesn't demand its own way.

When somebody says, “Ifyou love me, you would, ” we've left the realm of love.

It's not irritable.

It keeps no record of being wronged.

It doesn't rejoice about injustice.

It rejoices when the truth wins out.

It never gives up, it never loses faith, it's always hopeful, it enduresthrough every circumstance.

God says, “You have no idea what love is.

” Next, unloving behavior must be corrected.

Listen to me, parents, Iknow you love your kids, and so you excuse their behavior.

I want you to know that God loves you but He does not excuse your behavior.

Unloving behavior smut becorrected, Revelation 3:19, I correct and discipline every one I love.

You wanna know who said that? That's Jesus Christ.

You know, “That's not the Jesus I know.

” 'Cause you don't know Jesus.

Jesus Christ said, “I correct, “I discipline everyone I love.

” We live in a culture wherediscipline is not loving.

You know what's not loving? Not disciplining, it's not.

If you love someone, you haveto be willing to correct them, you have to be willing to discipline them.

Look, this week in smallgroup and our community group was one of the hardest groups we've had.

You say, “We're talking aboutlove, what could go wrong?” We were talking about love.

Love challenges, lovecorrects, love disciplines.

We had to throw downthe gauntlet this week in small group and say, “Look, man, some of you members “in the group need to do this now.

” And it was rough.

But that's what love does.

Colossians 3:19, husbands love your wives and never treat them harshly.

Listen to me, dads, ifyou don't want your kids to be disrespectful totheir mom, they why do you? Why do you? Never ever speakdisrespectfully to each other, remind yourselves.

Remind yourselves to howmuch you love each other.

Watch your tone, watch how you speak.

Proverbs 13:4, those who spare the rod of discipline hate their children.

Those who love their children care enough to discipline them.

Look, I'm not saying you gotta spank.

I'm not saying you gottahave a rod of justice in your house, that's not what I'm saying.

Every kid is different, every child is different, but lemme tell you something, parents, I know we have a problem in our church because I take your kids to camp.

(congregation laughing) And some of them, they don't believe the word no actually means anything.

Some of your kids hear noand they think it means go.

Every kid is different.

My oldest, all you hadto do was look at her.

Madison, (moaning), and she was repentant.

Broken down, “I'm sosorry, father, I sinned.

” My middle daughter, you couldlook at her all day long, you could yell at her, if you said stop, she would run.

Kid had a death wish.

I don't know what it was, you could talk to her until you were blue in the face.

(ranting) I just give up, come here.

Whack, right on the bottom.

It's like a reset button.

I don't know, it was like right here.

And she was like, “Yes, father, I do now understand.

” (congregation laughing) And I'm like, “Why, why, why do you have “to get the beating?” And she's like, “I don'tknow, I just need them.

” (congregation laughing) Then we had our son, right, boys are different.

You know what he did? He punched his mom.

Oh, I know.

(congregation laughing) I was like, (laughing), and I said, “Son, “you are not the son of my womb.

” (congregation laughing) I literally told him this, I said, “We're gonna make a memory.

” I know, and we did, it was good.

(congregation laughing) Now I don't wanna seeyou on CNN going to jail 'cause you beat your kids.

You're like, “Pastor MattBrown said that's the Lord.

” (congregation laughing) That's not what I'm saying, it's not what I'm saying.

But listen to me, you loveyour kids, the world won't.

You love your kids so you makeexcuses for their behavior, the world won't.

– [Congregant] Amen.

– And you need to help them understand that they need to behave in a loving way and love is patient, love iskind, love is not rude, mom.

It's not rude.

And you need to deal with that.

You need to deal with that.

I tell my kids all thetime, “Change your tone, “or I will help you.

” We gotta speak to each other in love, that's what the Bible says, “Speak truth to one another in love.

” Lastly, romantic love, romantic love must be directed.

You can't just follow your heart, you gotta give your heartto Jesus and follow His.

Romantic love must be directed.

We got a mom and a dad, and both of them areconcerned in their own way, so the mom says, “Oh son, son of my womb, “don't waste your life on women.

” The dad's like, “Bro, listen to me, son, ” right? 'Cause moms talk one way to kids, dads talk another way.

And you need both, you need both.

My son, pay attention to my wisdom.

Listen carefully to my wise counsel.

Why? For the lips of an immoralwoman are as sweet as honey, and her mouth is smoother than oil.

Here's what it means, parents, your little three year old, they're gonna listen to you to a point, and lemme just say, parents, raising children under five, you're in hell, but there'sthis beautiful thing, it's called six to 12, and it's wonderful, and it prepares you fornot-so-wonderful, it's called 13.

(congregation laughing) It's an unholy number.

I'm kidding.

(congregation laughing) But you gotta talk to yourkids while they still listen to you, because there's gonna be a point where they listen to erosand they tune you out.

My son, listen to me, payattention to my wisdom, listen carefully to my wise counsel, for the lips of an immoralwoman are sweet as honey and her mouth is smoother than oil.

And, oh by the way, so are guy's lips.

So are guy's lips.

But in the end, she is as bitter poison.

Just because you're thirsty, doesn't mean you should drink poison.

I know you want love, I know you do.

Let God teach you how todrink it, or you'll die.

In the end she is as bitter as poison, as dangerous as a double-edged sword.

Her feet go down to what? Death.

Her steps lead straight to the grave, for she cares nothingabout the path to life.

We call Sandals the Sandals Church because following Jesus is a journey.

We follow His sandals, wefollow in His footsteps, we follow in His life.

We do not follow the life andin the footsteps of others.

You are either on the path of life, or you are on the path of death.

She staggers down a crookedtrail, underline this, and she does not realize it.

Not everybody that'sgoing to hell realizes they're on the road to hell.

Some people think theyare on the road to heaven.

Stay away from her, don't gonear the door of her house.

If you do, you will lose your honor, lose your merciless, youwill lose to merciless people all that you've achieved.

Love destroys families, love destroys careers, love destroys life, if you're not careful.

Strangers will consume your wealth, and someone else will enjoythe fruit of your labor, and in the end, you will groan in anguish when disease consumes your body.

3, 000 years ago whenthe world knew nothing of sexually transmitteddiseases, God did, God did.

And some of you don't know this, but AIDS still takes more lives in America each year than guns.

They just don't advertise it.

Do you understand that? In our state, sexuallytransmitted diseases are at an all-time high.

Do you know why? Morality is at an all-time low.

And people don't walkaround with a, you know, flashing light on their forehead, “I have a sexually transmitted disease.

” That would be nice.

In the end you will groan in anguish when disease consumes your body.

Listen to me, whetheryou're gay, straight, or bi, God has a plan for yourlife that is different than your desires.

And we live in a world that said, “God would never give you erotic feelings “that He did not want you to act on, ” that is because they'venever read the Bible.

Or they have never read it honestly.

We all have erotic desires, that if we act on them, that if we follow them, they will ruin our lives.

Following Jesus will never ruin your life.

It will save your soul andit will bless your life.

Some of you guys don't know this, but the man who is accreditedwith writing these words, his name is Solomon.

The Bible says he isthe wisest man on earth, and we know he was the stupidest man when it came to women.

You see, he had wisdom in some areas and he was ignorant and foolish in others.

It's why his wife, at the end, says, “Do not ruin your life “as some kings do.

” Because Solomon ruined his life because he followed the desires of eros, rather than the desires of God.

Here's what he says, here's a guy who's had thousands of women, thousands of sexual escapades, here's what he says to his son.

He says, “Drink water from your own well, “share your love only with your wife.

“Why spill the water of yoursprings into the streets, “having sex with just anyone? “You should reserve it for yourselves.

” He's talking about marriage.

“Never share it with a stranger.

“Let your wife be a fountainof blessing for you.

“Rejoice in the wife of your youth.

” As you age, you don't look the same.

That's true, it's why Godblesses us with poor eyesight.

(congregation laughing) You just remember.

(congregation laughing) He says, “Let your wife be afountain of blessing for you.

“Rejoice in the wife of your youth.

“She is a loving deer and a graceful doe.

“Let her breasts satisfy you always.

“May you always becaptivated by her love.

” Tammy and I were at a meeting last week and she was running themeeting and I was listening.

And there were just a couple of moments where I caught her outof the corner of my eye and I remembered when she caught my eye, almost 30 years ago.

Here's the truth about marriage, it's a lot of work, it'sa lot of challenges, and there's not alwaystime for eros and romance, but there are moments.

And I saw her and then I watched her and then I saw it again, and then I saw it again.

And after the meeting we drove home and I said, “Tonight, babe, while you were talking “and while you were running the meeting, “I was blown away athow beautiful you are.

” We've been married 24 years.

I watched her sink intoher chair and gush.

And she said, “You have no idea how much “that means to you, to me.

” She said, “I love hearing “that you still think I'm beautiful.

” And I said, “This isgonna be a good night.

” (congregation laughing) (congregation clapping) Right? The old buck is awakened.

(congregation laughing) Listen to me, this iswhat God wants for you, God wants you to be committed to someone who is committed to you.

No matter what, throughgood times and bad, for better or worse, until death do you part.

You see this ring that I wear? It's a commitment, notjust to her, but to God.

– [Congregant] Amen.

– And I plan on wearing thisuntil death takes me home or death takes her home, because that's what agape love demands.

It's what God has for you.

(congregation clapping) Amen? (congregation clapping) And I know some of youdon't believe it's possible and that's because you don't know God.

You don't know God, you have no idea what He has in store for you.

If you wanna experience this love, you have to make a commitment today to listen, to listen.

And Jesus was asked what's themost important commandment, some of you know it, does anybody know it? Say it out loud.


Love the Lord your Godwill all your heart, soul, mind and strength.

That's the Christian version.

In Hebrew it begins with a different word.

Listen, it's called the shama.

When Jesus is asked what's themost important commandment, He recites the shama.

And shama in Hebrew means listen, listen.

Hear, oh Israel, listen, oh Israel, the Lord your God is one, and you must love the Lord your God with all your heart, allyour soul and all your mind.

You see love begins with listening.

Let's pray.

Heavenly Father, we thank You for today.

We thank You for the opportunity to listen to You.

We pray in the mighty name of Jesus, God, right now, that Youwould heal broken hearts that have been shatteredby love, broken by love, and betrayed by love.

And I pray, right now, theywould make a commitment to listen to Your love, to listen to Your commands and to learn from You.

And, Lord, for those who are single, I pray that they develop alist and it starts with this, they will not marry or date anyone who does not listen to You.

I pray this in Jesus name, amen.

Love you Sandals Church.

Hey, I'm Pastor Matt.

Super excited and thankfulthat you took time to watch any of the contenton sandalschurch.


I would love to invite you to be a part of just those who support theministry at Sandals Church.

Look, I realize many ofyou go to other churches and I'm not encouragingyou to take any money away from that, but any amountthat you could give to help us continue toprovide this content online for free, that's theheart of Sandals Church.

And some of you, man, you're not a Christian, but I you watch this, andyou're feeling led by God to give something, any amount helps.

It helps us continue toprovide this content online, and I just am so blessedthat you would just take time to pray about it.

And all gifts are welcome.

Thank you so much for helpingSandals Church teach people how to be real.

(upbeat music).

Healing Past Hurt | Sandals Church

(bright music) – Hey everybody, welcome to Sandals Church where we are all aboutthis vision of being real.

And if you wanna divedeeper into this vision or even what it looks like in your life or ask any questions.

Head on over to Debrief.


It's our podcast thatyou have to check out if you wanna learn moreabout what God is doing through Sandals Church.

But thanks so much for joining us today.

Enjoy the message.

(upbeat music) – Hello Sandals Church.

I also wanna welcome thoseof you who are joining us via Sandals Church TV.

And so it's good to behere with you today.

I don't know if youwere with us last week, but we've begun this new series called “The Cure For Loneliness.

” And Pastor Fredo kind of opened it up and presented the problem.

And that's this: That there is an epidemic of loneliness not only in our country, but across the globe.

We're seeing staggering statistics that reveal this problem ofisolation and loneliness.

In fact I was thinking about it this week.

Like when did I feel the loneliest that I've ever felt in my life? And I had been over the deepend for a couple of years in high school, partying quite a bit.

And I knew I needed to get away.

I needed to change my environment.

And so I went to college in Oklahoma and it was the first weekend of classes.

They had this special little event thing, The Last Day of Summer they called it.

And we went to this waterpark in Oklahoma City.

And before the park had opened there was this sort of side picnic area, some volleyball tables, volleyball tables, that was strange.

Volleyball courts.

And we were playing thispickup game of volleyball.

And all of the sudden Istarted to get lightheaded.

Started to get dizzy.

And the world around me began to spin.

And the next thing I knew Iwoke up strapped to a stretcher getting put in an ambulance.

I had no clue what had happened.

I had to be told that just 10 minutes ago I had a grand maul seizure.

I'd never had a seizure before in my life.

As far as I knew I wasn't epileptic.

I got rushed to thehospital, ran a buncha tests and all of these kinds of things and I remember just sort ofbeing as alone as I'd ever been.

I was 1600 miles from my home, anyone or anything that I knew.

And I remember I finally criedout to God in my loneliness.

It had been awhile since I'dengaged the God that I knew.

And so I know that thatinternal experience of loneliness andisolation, even in a world where we might be around alotta people, is very common.

But it's something I wouldnever wish on my worst enemy.

And so what I love thoughis that Pastor Fredo didn't just leave us there.

He pointed us to the solution.

And that's this idea thatthe cure for loneliness is a table.

It's a table both in the literal sense that it's a space that wegather around, we share a meal, it's a space where we getto share about our days and what's going on in our lives, our frustrations, our joys.

But it's also sort of thismetaphor that we'll be using over the next several weeks that really is a metaphorfor the space within which the kind of community, the kind of humanflourishing in relationship that God wants for us, that's where this happens, at the table.

And so the idea for therest of the series though, is to actually unpack thosethings that get in the way of us getting to the table.

What are the things that keep us isolated? Relationally? Maybe you've been at the tablebut you've been displaced for one reason or another.

Maybe you've been dismissed, right? There's a circle of friends that you're just not welcome anymore.

Maybe you've dismissedyourself because you believe, man I don't know if beingat the table is worth it.

People at the table are crazy, right? And maybe you've justsorta, or you've been hurt and that's really sortof the topic for today.

Is maybe you've been wounded at the table.

And so maybe you didn't ask to be excused but you just sort of slid your chair back, hoping nobody notices andjust sort of walked away.

And so how do we get back to the table, especially when we'vebeen hurt at the table? And so before we jumpinto our message today, I'd just ask that you'dpray with us, pray with me that we would have God's help as we sort through his word together.

God we are so thankful that you have not left us to ourselves.

God that you have givenus your word as a guide and my prayer is that youwould give us ears to hear, and God that you would alsojust be with me as I deliver it, actually feeling a littlebit off physically, God, so sustain me, give mestrength and energy.

And God would we have earsto hear from your word and be changed by it today.

In Jesus' name we pray, amen.

So here's kind of the firstthing I wanna share with you.

God's original design, the plan for the table was actually this divine institution from the very beginning called the family.

That was the space that Godintended for us to be safe, to be known, to find intimaterelationship with one another.

But ever since the gardenof Eden, the family table, that space has been broken.

And so each and every one of us, even if you had a good familyenvironment growing up, maybe both of your parents were present in the way that they were supposed to be and you say yeah, actually mychildhood wasn't all that bad.

There's still some brokenness.

Every family's got it.

And so what happened along the way is that we got hurt, right? And so there's a reason thattherapists spend a lotta time just going back to childhood stuff.

Childhood stuff.

And so the story thatwe're gonna be a part of and jump into today is actually the story of a broken family.

And it's a crazy story.

It takes up about thesecond half of Genesis.

And so before we jump into the passage I need to give a little bit of context.

There's this guy named Jacob.

He needs a wife so his familysends him to a different town to some relatives and hemeets this gal named Rachel.

And the scriptures say thatRachel had a beautiful figure and a lovely face.

She was hot, right? She was fine, all right, okay? He was into her, okay? And so he approaches her dad, named Laban, this guy named Laban.

And he says “Man, I wantyour daughter, Rachel.

” And so he says, “That's fine”.

“You gotta work for me for seven years.

” And so if you're a romantic or you're into cheesy love stories like it's actually a very powerful story.

It says this, the Biblesays this about Jacob and his love for Rachel: After working for seven years, right? He loved her so much itseemed as if but a few days.

(congregation laughs) Right? And so he goes to marry her and Laban, this yahoo, he actually tricks, he dupes Jacob and onthe night of the wedding gives him actually hisolder daughter, named Leah.

Now here's what the Bible in one translation says about Leah: She didn't have asparkle in her eye, okay? Let me translate that for you.

This is the Bible's kindway of saying that Leah, she was U-G-L-Y.

U-G-L-Y, right? She had no alibi.


But he wasn't into her.

But he loved Rachel andso he ended up working a whole another seven years.

And if you thought your family was crazy, think of four moms.

Not just one pair of, one sister wives, right? But two pairs of sisters wives.

There was some maids involved too.

There were four moms thatended up having 12 sons.

In fact these were whatwe would then later know as the 12 tribes of Israel.

Because Jacob's namewas changed to Israel.

It was literally Jacob'ssons, the 12 tribes of Israel.

And so that's where we pick up our story.

And this story is one of the longestnarratives in the Bible.

It's actually from chapters 37-50.

It's a beautiful story, the story of Joseph.

And so that's where we pick up.

This is the account ofJacob and his family.

When Joseph was 17 years old, he often tended his father's flocks.

He worked for his half brothers, the sons of his father'swives Bilhah and Zilpah.

You gotta love the Biblical names, right? Bilhah and Zilpah.

But Joseph reported to his father some of the bad thingshis brothers were doing.

Most of you, if you knowthe story of Joseph, you'll know that most of it is about what his brothers do to him.

But I think we forget thatit actually starts with him.

He's a punk little brother, right? He begins with tattle taling, right? He's reporting to his father the bad things his brothers had done.

I've got four sons.

So I'm very familiar with brotherhood, and the many sorts offights and different things that go on amongst ourbrothers or our sons, the four brothers.

The third one, named Asher, coincidentally it's one ofthe 12 tribes of Israel, came into my room theother day and he's giddy.

Like he's like (laughing)like dancing like, you know just a weird kind of happy.

I'm like, what is going on with you? And he begins to share with me that he got this legendarycard in this game, like this digital game, Clash Royale, if you care.

And so he got this legendarycard and I'm just like man, your excitement level, it doesn't quite match.

Like I don't understandwhat's so big about this card.

And the truth actually came out.

It wasn't so much that he washappy that he got the card.

It was that his two older brothers didn't have that card yet.

Right? It's just kinda how brotherhood works.

A punk little brother Joseph is, right? And so Jacob loved Joseph, this is the dad now, not only does that hurt his brothers, I'm sure they're not fansof the tattle taling, but then you've got thisother layer from the dad.

Jacob loved Joseph more thanany of his other children because Joseph had beenborn to him in his old age.

So one day Jacob had aspecial gift made for Joseph, a beautiful robe.

The thespians in the room might know this as the amazing technicolor dreamcoat.

Got three theater fans in the room.

Probably wasn't technicolor.

It's a beautiful robe.

A gift from his dad to his favorite.

But his brothers hated Joseph because their father loved himmore than the rest of them.

So we've got another layer of hurt for the other 11 brothers, right? A dad who clearly favors his son.

And we know not only thatit's that the sons that he had in his old age, but him andhis other brother, Benjamin, who he also favors, they were, those two, they were the sons of Rachel.

There's another layer there.

But this is what it developed into.

They couldn't say a kind word to him.

Like they were so offended that they couldn't say a kind word to him.

When Joseph's brothers saw him coming, they recognized him in the distance.

As he approached, theymade plans to kill him.

That escalated kinda quickly, right? Made plans to kill himas they saw him coming.

The first point in your notes as we look at this story about this family that's displaced, this broken family table, hurt people hurt people.

Maybe you've heard that phrase before.

People who are wounded, who are hurt, it's kinda the notion of like, don't bite the hand that feeds you.

When you're wounded, when you'rehurt you tend to lash out.

In fact it's whatperpetuates the cycle of sin.

We are sinned against, we're offended, and then we sinfully respond to that.

And so goes the cycle.

You know my oldest son, he's a super sweet kid.

Well loved, we're reallyblessed to have him as a son.

And when he was a toddler he was so sweet that he went through this phase where if he bumped intosomething like the coffee table he would be like “Sorry.

” Aw, right? Yeah, crazy sweet boy.

Just loved everybody, super kind.

Until one day, as a three-year-old, he got a splinter in his hand.

And my son's not a wuss, but he gets a little dramatic with pain.

Like he just, you knowhe was freaking out.

And for whatever reason, whenever something crazyhappens at our house, when chaos is unleashed, I'm not there.

My beautiful wife gets to dealwith the crazy by herself.

We had a kitten go into seizures once.

Where was I? I was on the lake.

My kids are freaking out.

Their kitten, I know, that's kind of dark.

But there was a moment, I'm not kidding you, where a bat got into our house.

A bat.

Circling our house.

And they're freaking out.

Where was I? Not there, you know? So my son gets this splinter and my wife calls me and I can't hear her because all I'm hearing is screaming, like bloody murder in thebackground, like (screams).

Like just a demon child, right? And I'm like what iswrong, like is Avery okay, is he dying, she's like”No, he has a splinter.

” It's like all right, I'm gonna come home, try and help you out.

So I get home and he's just not having it.

She hasn't even touched himwith tweezers yet or anything.

And so we're like buddy, we gotta get this out.

Da da da da.

I found out later, like wedidn't have to traumatize him in this way because it'll come out and make its way to the surface, but we were wanting toget the splinter out.

And so we're like startingto kinda restrain him or whatever and he is scream, he is like everythingthat he can muster up in his tiny little three year old body.

And then this sweet little boy, just spewed the most venomous curse that he could come up with.

He looked right into my soul.

He pointed at me, he said, “You are an ugly, ugly man.

” (congregation laughs) I was like, oh, I'm not evenyour dad anymore, right? You have to refer to me as some other man.

And I'm ugly, right, apparently Leah wasn't the only ugly one.

Like I'm like whoa okay.

We probably added insult to injury.

We laughed so hard.

We'll be paying for that therapyfor years to come I'm sure.

But the point is this, he was hurting.

Right? He was hurt.

And so he lashed out with hurt back at me, the one who was tryingto take care of him.

And so my question to you today, is have you dealt, weall have them by the way, have you dealt withthe hurts in your past? Have you dealt with yourown broken family system that displaced you from the table, the very space that wassupposed to teach you how to be in a real relationship, in true community.

Maybe you haven't yet done that because you don't know where to begin.

Maybe there's a lotthere for you to unpack.

And so maybe that'sbecause of this next point in your notes, is this, is resentment multiplies the hurt.

Resentment multiplies the hurt.

And when you hear the word resentment you can plug in a coupleof other synonyms there.

Bitterness, unforgiveness.

It compounds the original issue.

So as if the originaloffense wasn't enough, now this stuff starts to happen internally and it multiplies the hurt.

I was talking to my thirdson about the message and about this idea of pasthurts and how it isolates us.

And he's like, “Ohyeah, like Spider Gwen.

” Now if you're old likeme or you haven't seen “Into the Spiderverse” yetit's the story of this girl, she's sharing how her bestfriend, Peter Parker, got shot.

And she wasn't able to save him.

And so she says, “Now I end upspending the rest of my life, “now I'm just saving everyone else.

” But then she says thisone really telling line, and my son, my 11 year oldson, is sharing this story, he gets it.

She said “And now Idon't do friends anymore, “just to avoid the distractions.

” You see the resentment from the loss of herbest friend being shot had kept her from being in relationship.

It's this powerful pictureof somebody who's wounded and is actually trying todo what's right, right? She's trying to do the super hero thing.

But she's not about friends.

She's not about community.

So we pick up our story, but before we do that, there's a few chapters that have been skipped.

And so what ends up happening is the brothers havethis plan to kill Joseph.

They leave him in a pit.

And then they say, 'cause they were like ah Dad would be really ticked at us.

We don't want that blood on our hands.

And so they throw him in a pit.

So the wild animals'lleventually get to him.

But then they see some traders going by and they say well hey, let's profit on this deal.

They sell him to some traders.

He gets shipped to Egypt.

He's falsely accused andthen starts to rise to power because God's given him thisgift of interpreting dreams.

And the Pharaoh, the king of Egypt, needs some dreams interpreted.

But then there's a faminein the land of Israel.

Right? And his brothers, they are sent by Jacob, to go get food for the family.

And now, now's thattime to exact vengeance.

It's telling, the initialresponse is as we read it.

Since Joseph was governor of all Egypt and in charge of sellinggrain to all the people, it was to him that his brothers came.

When they arrived, they bowed before him withtheir faces to the ground.

Which by the way, is thefulfillment of a dream that he'd had years prior.

Joseph recognized his brothers instantly, but he pretended to be a strangerand spoke harshly to them.

“Where are you from?” he demanded.

“From the land of Canaan, ” they replied.

“We have come to buy food.

” So right, this is the firsttime he's seeing his brothers after they've left him for dead.

And I think often ourinitial response to something is the most telling one.

Clearly there's some resentmentstill there with Joseph.

And it's multiplying the hurt.

Now God begins to work on Joseph's heart after this point in the story and things begin to shift.

And we'll get there soon.

But I'm just reminded ofhow we can hold onto things.

My oldest son, that same sweet boy, again talking about this idea, preparing for this message.

And he said, talking about past hurts, he's like “Oh yeah, you mean that time “you forced me to go on Tower of Terror?” (congregation laughs) So if you're California Adventure, it used to be Tower ofTerror, now it's Guardian, it's one of these like dropsort of rides, you know.

And we were there and I'm like, he's probably eight years old at the time.

And I was like, yeah manyou gotta go on this.

And he's like nope.

Right, he's digging his heels in, he's like I'm “No, I'mnot doing it, too freaky, “too scared, no way.

” But I was like, no, no, no, internally, right? I'm like I know how this story line goes.

Like I pressure him and pressure him and then he goes on the ride and he loves it and hewants to do it again.

So that's what I'm gonna do.

Right? Come on bud.

Like it wasn't peer pressure, Dad pressure, whatever.

And finally he succombs, right? I mean he's like “Okay, I'll do it.

“I'll do it for you.

” Right? So he's retelling this story.

He's like “Yeah, Dad, that's the day “that my fear of heights began.

” (congregation laughs) Like, right? And he's actuallymentioned it a few times.

And I'm like wow, like you'restill bringing this up.

And he's kinda joking, maybenot joking a little bit too.

And so I'm starting to realize, man I need to have a conversation.

I need to figure this out.

I need to make some things right.

He's like “Oh yeah, and a few days later “we were playing catch andyou threw a tennis ball “and I didn't catch it andit hit me in the face.

” I was like oh my gosh.

It was a rough week for Avery.

And so like we ended uphaving this conversation about that.

But I could tell that there was still, even if it was low level andwe could laugh a little bit there was still something there.

There was still a littlebit of bitterness there that's this thing thatI did to my own son.


And so I wanna actually takea little bit of a left turn, it's gonna feel likethat, but stick with me.

Because I wanna shift tosomething a bit more serious.

I wanna talk about what we'vebeen experiencing as a nation.

Many of you know lastweekend there were two more mass shootings in our country.

Leaving 31 people dead.

And so with all of the onlineand digital and social media sort of venom that gets spewed.

You know you're scared almostto like what do you say? Right? The whole idea of thoughts and prayers, like that's been criticized.

We have to act but whatcan we possibly do, right? It's a huge problem.


It's indicative of acultural rift in our country, like what do we? Okay, if we're supposed to act, what could we possibly do? Right? I'm with Pastor Matt, theidea of sending thoughts is a little strange.

What about the prayers? And I had to, I came to a point this week where I was convicted of this.

I had to ask myself the samequestion that I would ask you, because I have this personalcommitment that as a pastor I'm not gonna say I'mpraying for you if I don't.

Like it's just, we say that a lot, we throw it out and I'm wondering, has that become cliche, isthat just something we say? Or church are we on our knees? Are we actually praying? And I confess, it was about Wednesday, several days afterwards, where I finally realized, man I haven't, I haven't prayed.

And so I did and I was reminded, like man where do you even begin.

I remember Romans 8 that says this: When we don't know how to pray, the spirit intercedes with us with groans that words can't express.

And so I do believe that the church is called by God to play aprophetic role in our culture.

And by prophetic I don'tmean telling the future.

I mean reading the signs of our times and delivering God'sword, God's truth to it.

And so the first thingI wanna say is this: Is you need to know thespirit of God is grieving.

And he's praying with groansthat words cannot express.

But I wanna offer one more thing.

And it's the next point in your notes.

It's the way forward, it'sthe way back to the table.

The way back to the tableis through forgiveness.

The way back to the tableis through forgiveness.

My guess is, it's like maybeyou're a little jarred, you're like what does forgiveness have to do with a mass shooting? Forgiveness, like isn'tthat a little weak? Like gimme something with alittle more teeth, Pastor.

It was enough, forgiveness was sufficient for a community inPennsylvania 13 years ago when a lone gunman walkedinto a one room school house in, of all places, an Amish community.

Like a people of peace.

He took 10 girls hostage, ages six to 13.

Shot 10 of, excuse me, shoteight of them and five died.

What we would find out later as the investigation went on was that this man had helddeep resentment against God because nine years prior he had lost his own infant daughter.

Talk about resentmentmultiplying the hurt.

But that's not the end of the story.

And what would ensue withinhours after that shooting blew the mind of our nation.

What ended up happening within hours is that several from the Amish community, some of the elders, went to the home of the now widowed gunman'swife to extend forgiveness.

To say look, we'regrieving, we're in shock, but I gotta imagine so are you and your three young children.

Right? And it doesn't even stop there.

Their forgiveness wasmore than just verbal.

They put their money where their mouth is.

They raised a fund forthe family of the gunman, the family of the gunman.

Right? Like what? Like who does that? And some of us are evenlike man, that feels wrong to move so quickly to forgiveness.

But here's what it did: it's a powerful force relationally.

It healed the community.

This week, my wife, Shanalea and I, we were watching a movie based on it and the production value's not great, the acting's not great, but about halfway through my wife is just like bawling.

You know even at several moments, like I'm tearing up.

At one point she slaps me.

She's like “Why did youmake me watch this?” Like she's just a wreck.

You know? Like you're gonna haveto forgive me for that.

That's violent, you know? But it was powerful, this story.

The way back to the tableis through forgiveness.

And so in Genesis 50 the brothers have beentaken care of by Joseph but finally their dad, Jacob, dies.

And they're probably thinking, like man, Joseph and his kindness and his taking care ofus, it was all for Dad.

But what ends up happening is Jacob dies.

But now that their father was dead, Joseph's brothers became fearful.

“Now Joseph will show his anger “and pay us back for allthe wrong we did to him.

” He will take vengeance.

The opposite of forgiveness, right? He's gonna stick it to 'em, they said.

But Joseph replied.

Listen to this perspective.

“Don't be afraid of me.

“Am I God, that I can punish you?” In other words he understandssomething very deep about forgiveness.

It's not that it just sort ofgoes away into the atmosphere.

It's actually transferringit to the ledger of God.

God will ultimately take an account.

In the Amish community, they said man, your husband is gonna standbefore a holy and just God, have mercy on his soul.

They knew that there's one seat, one who can occupy that seatof judgment who is righteous.

And we're gonna give ouroffenses, our wounds, our past hurts to him.

We're gonna allow him to deal with it.

Joseph knows whose place that is.

It says this then in the next verse.

This is one of the most beautiful verses in the Bible, I believe.

Especially when it comes to a picture of extending grace and forgiveness, and redemption thatcomes when that happens.

“You intended to harm me, butGod intended it all for good.

“He brought me to this position “so I could save the lives of many people.

“No, don't be afraid.

“I will continue to take careof you and your children.

” He too puts his money where his mouth is.

And then check out howit comes full circle.

I encourage you, go home and read this.

It's 14 chapters.

Comes full circle.

He says this: So he reassured them byspeaking kindly to them.

It was his brothers that couldn'tspeak a kind word to him.

And now because of this work that God does in Joseph's heart, this perspective that he's brought, allows him to forgive them and to speak kindly to them.

Ephesians 4 says this: Get rid of all bitterness, rage, anger, harsh words and slander, as well as all types of evil behavior.

Instead be kind to each other, tenderhearted, forgiving one another.

It's a brief pictureof very concise picture of what it means to be at the table.

The kind of communitythat God is creating, that Jesus is inviting us to, is one that is tenderhearted, that is kind, that is ready to forgive.

But how? Or maybe the better question is why, like why forgive? Like what's the motivation here? It comes in that next clause.

Just as God throughChrist has forgiven you.

Remember what Pastor Fredo said last week, to be at the table is to know that you are a sinnerin need of repentance.

Your ability to forgive comes from a clear understanding that you yourself are asinner, capable of doing evil, a capacity to hurtsomeone, to offend someone, even if you don't mean it.

Perhaps you've understood that you've said or done something relationally that has caused somebody elseto take off from the table.

And so what do you do but toextend that same forgiveness that you've been shown? We only have a seat at the table because Jesus has first forgiven us.

And now we have no choice if we get that to do the same for others.

So I wanna talk, I just wanna unpack for ourlast few minutes together, a little bit about what forgiveness is, what it isn't, somepractical kinds of things to clarify from God's word howyou might go out from here.

Not just a hearer of theword, but a doer of it, to be people, a church, marked by forgiveness.

I wanna give you a quick definition first.

Most of the, a lot ofthe Biblical passages about forgiveness usethe metaphor of finances.

It's actually a notion of debt, of owing someone something.

In fact in one version, onetranslation of the Lord's Prayer it says forgive us our debtsas we too forgive our debtors.

So the quick definitionI would give you is, forgiveness is about declaring that though you have wrongedme, you don't owe me anything.

You don't owe me anything.

And so I'm releasing you from that debt.

It's a radically different system than the one in the Old Testament, an eye for an eye and a tooth for a tooth.

You do something to meyou have to pay me back with an equal amount.

And forgiveness here is about saying you don't owe me anything.

The political party that you're mad at, they don't owe you anything.

The oppressive system, thoughit's oppressive and evil, it doesn't owe you anything.

You're releasing that, you'resaying that's on God's hands to deal with.

And so there's a few things.

Forgiveness does notmake what happened okay.

Forgiveness does notmake what happened okay.

So as we've had a lot ofopportunities with four boys to practice making anapology and things like that, we've taught them that whenthey say they're sorry, first of all they have to name the wrong I'm sorry for.

And the more specific themore effective the apology.

Right? Not just a general, like oh I'm sorry, like my Dad's making me do this.

Right? Sometimes I really get them andI make them hug for like 10, I literally count out 10 seconds.

And so it's actuallyamazing what happens by, like they're all like rigid and whatever, and I won't start counting until they're actuallyembracing each other.

And by about six, seven or eight, as I'm counting to 10they're like laughing.

It's pretty amazing.

But what's the most commonresponse to an apology if you think about it? Somebody comes to you andthey say, “Hey I'm sorry.

” Most of us say, it's okay.


That cheapens the forgiveness.

What happened isn't okay.

I didn't list all ofthe Bible verses there.

My hope is that you'd go homeand unpack some of those.

The one that you see underthis point is Isaiah 5:20.

It says woe and not like whoa, but like Biblical woe, likewoe, like bad things upon you.

Right? Who call something that's evil good.

But we're not asking of you, what God isn't saying is to forgive is to callsomething that was wrong, good or right or true.

And especially, there'sa spectrum of offenses.

There's sorta the petty every day stuff and I'll speak to those in just a minute.

But then on the other end of the spectrum there's some pretty deep level wounds that some of us are carrying, some hurts.

Those of us, for instance, who've been abused.

Emotionally, verbally, sexually, maybe all of the above.

And so what we're not saying is that what happened to you is okay.

Far from it.

So what if the other person though, doesn't acknowledge the wrong? You say you don't owe meanything, it's forgiveness.

But don't they at least owe me an apology? How many of us are stillwaiting on that apology? That's probably never gonna happen.

And so does forgivenessmake sense in that context? Where we don't even know if the person who wronged usknows that they wronged us.

Forgiveness can also be oneway, that's the next point.

Forgiveness can be one way.

Now when it's wise, or when it's safe, there's another layerthat the Bible speaks to called reconciliation.

It takes two to tango with that.

There has to reciprocity forrelationship to be restored.

Right? But with forgiveness it can be one way, because here's the deal.

As you've been hurt and you're trying to makeyour way back to the table, you may not be coming back to the table with the people who hurt you.

You're trying to get back to the table because you need community, it's how we're designed to live.

And so forgiveness can be one way.

I know that because themost profound picture of forgiveness we haveis Jesus on the cross.

And one of his last words is this: “Father, forgive them, theyknow not what they do.

” The people who were crucifying Jesus and theologically by the way, that's me and you and everyone else.

They didn't know what they were doing.

He didn't wait on an apology to ask his father in heaven to forgive.

Forgiveness can be one way.

Also forgiveness is costly when it's a death to self.

Like we have to choose to not hold onto what's rightfully ours, it costs us somethingto sort of absorb that or to release that.

But it's not optional Matthew 18 tells a story about this guy who owes an unpayable debt, like think millions andmillions of dollars.

And he's about to getin some serious trouble 'cause he can't pay.

I think he's about toget throw into prison.

And so he's begging formercy from this king, from this master, thislord who he owed money.

And finally the king has mercy on him, the one who's owed the money, and he says, yeah actually, I'm gonna just forgive this.

You don't owe me anything.

And he walks out and the sameguy who was just forgiven sees some other knucklehead on the street who owes him a fraction ofwhat he was just forgiven.

He's starting to like choke the fool out, trying to get his money back.

He just came from being forgiven, right? That's a picture of me and you.

We've been forgiven and so we don't, it's not optional as a Christian.

Should I forgive or not? It's just what we do.

And I know that that'sa hard word to receive.

But ultimately it frees you.

It heals you, it allows youto come back to the table where there are people who are safe, who maybe won't wound youas you've been wounded.

Finally I'm not naive.

I know that even though there's a moment where we choose by our will to forgive, and I wanna emphasize that really quickly, don't wait 'til you feel it.

I'm finally feeling like forgiving.

It probably isn't gonna happen.

Most things that God calls us to are acts of our will.

And we pray that the feelings follow.

Right? But it's a process.

One of Jesus's disciples says”How many times do I forgive?” And if you know this story, Jesus says, “70 times seven.

” Some of the mathematicians are like 490.

Some of you are like myhusband's long past 491.

I don't have to forgive any more.


It's not the point, right? The idea is just to be aChristian, to follow Jesus in this way is to forgive andto forgive and to forgive.

Indefinitely, as long as it takes.

The last point in your notes is this.

Forgiveness moves us fromvictimhood to victory.

From victimhood tovictory because some of us are real victims.

We've been hurt.

And yet the victory is when we can berestored to relationship, when we are able to dealwith that and heal from that in such a way that wecan be back at the table.

And I mean let's be honest for a moment.

Most of like the offenses in our lives, not to minimize the stuff onthis side of the spectrum, that's very serious and it'svery real, that's very deep.

But most of the offenses arelike the day to day stuff are really kinda petty, right? It's almost in our culture, like we're just waiting to be offended.

The other day, yesterday actually, I was in a parking lot, busy parking lot.

I was in a hurry.

And the rest of the world apparently didn't know I was in a hurry.

And this guy, there was an open spot and I'm like it's kindaclose to where I'm going.

And so he jumps in ahead of me.

And then if like thatwasn't enough, right? He added the insult to injury and decided he wanted todo like the back in thing, facing forward.

And then he didn't get his angle right, so it wasn't just like a three point turn but where it's like thisguy doesn't care about it.

And then I'm like ohthere's the guy behind him that's gonna take my other spot, right? And I'm all offended.

You know? I'm like oh my gosh, you know, just this morning I wentto go to the refrigerator, to grab my wife her Half &Half, her cream for her coffee.

And she thought I waslike getting in the way and it's like 6:30 a.


, right? And neither of us have got our coffee and we are not even lovingJesus at this point.

(congregation laughs) And she is like, I openthe refrigerator door and it like cuts her off and she's like, gives me kinda just this likestink eye look or whatever.

And I'm like I felt it, like I'm so offended.

I'm here to serve you, likeI'm getting your cream, girl.

(congregation laughs) Offended, right? What if what we brought to the table was an olive branch? The olive branch is asymbol, Biblical symbol for relational peace, for the extension ofgrace and forgiveness.

What if this was just in our back pocket? Right? And I'm in community group and I share something and it'svulnerable and I perceive, like you didn't handle my heartwell, it's just ready to go.

Because ultimately it's not about me, it's about the table.

It's about this space, it's about this community.

And so what I love is these elements for the next several weeksare gonna stay on the table.

I love that we started last week with the two glasses of wine and bread that's actually not wine, we're Baptists.

It's grape juice.

But it's the symbolic presence of Christ.

And it's the centerpiece.

It's that which allelse around it revolves.

It's what makes the table possible for us.

And so we've gotta get usedto bringing forgiveness, relational peace, we gotta make allowance for each others' faults.

I've already accountedfor it, you're good.

I forgive you.

I'm just quick to move there.

So that the table doesn't get disrupted.

Because here's the beautifulthing about the table.

Is that this is practice for a forever table of Jesus.

Do you know that the Biblespeaks of our future hope as a big party, as a banquet, as a feast.

There's a table and it's really big and here's why I know it'sreally big because in Matthew 8 it says that people fromall around the world, from the East and the West, people very different from me and you are gonna sit around this tableand share a meal together.

United by Christ.

Marked by forgiveness.

Would you pray with me? God I wanna pray a prayer that your son Jesus taught us to pray.

Forgive us God, of our sins.

As we forgive those whohave sinned against us.

God would we be a people united by Christ, invited and sitting at the table because we've been forgivenand therefore we're ready with the olive branch, we're ready to forgive.

It's our first move.

And so God we do pray thatwe would leave from here, not just having heard your word, but doing it as a church that people would look at Sandals Church and be like what grace, whatmercy, what forgiveness.

I wanna sit at that table.

And that we would invitethem to this understanding that they will one day, if they choose you, to sit at a table that will last forever with people from allnations, tribes, languages.

Enjoying the feast that is ours in Christ.

In Jesus' name we pray.


– Here at Sandals Churchwe really do believe that this vision of beingreal can change the world.

Because Sandals Church is a nonprofit that operates from donationsfrom people like you.

Because when you donate yourmoney goes to creating places for people to be real all over this world.

So man, I would love foryou to be a part of that and you can make a donation today by clicking the link on this video or going to donate.


So join us, and join what God is doing through this vision of being real and have a great day.

(bright music).

6 Favorite Minimalist Sandals (After 3 Years)

What is up? Chris Cage here, founder ofGreenbelly Meals.

I've been wearing minimalist sandals almost every day for over three years now.

I'm a big fan of these things.

Today I'm gonna talk aboutthe six brands that I've been wearing.

We've got Earth Runner, Xero Shoes, Bedrock Sandals, Luna Sandals, Unshoes and Shamma sandals.

Alright, hopefully myfeet are clean, toes a claim for you.

In no particular order starting off withEarth runners, the Alpha adventure model I love them.

Wore them for about six months.

My favorite thing about these is the canvas footbed.

Super super comfortable.

Minimalist straps make it easy to get in and out of.

Foot just nestles in there.

They do get a little oily from your feet but I noticed that they clean up prettyeasily after a walk on the beach.

now one thing that Earth Runner seems to reallypush is this concept of grounding See this copper plug right here? Supposedly it helps connect you more to the earth.

I don't know any of the science behindthat.

Just something to note One thing that did throw me off about thesesandals was this strap right here by the front toe this thread was a little toughwhen I first got it and left some red marks on my feet after a few days itbroke in fine so not a big deal if it fits and feels great now.

Next up Xero Shoes.

This is the Z-Trail model.

I really love this model.

The Z-Trail are the only shoes on this list with the horizontal non-thong strap.

I did have the Cloud from Xero Shoes which had a much thinner sole and a thong strap.

I really prefer these Much less flimsy My toes don't feel cramped at all uphere The footbed is very very comfortable I love the lip around thisedge right here It seems to help keep debris out more when I'm outside.

Overall, just great lightweight and comfortable sandals One tiny gripe is that thisstrap requires you to really slide your feet all the way up on the sandal beforebeing able to get it on.

Not a big deal.

Just takes an extra second to get that heel strap on.

Next up Bedrock Sandals This is the Cairn modelBedrock's flagship model.

Bedrock is doing something really interesting They're kind of the halfway point between a real thin minimalist sole sandal and a clunky Chaco style sandal.

They've got the thinner sole and zero drop like a minimalist sandal but are much more rugged than anything else on the list and make a really great hiking sandal I've seen a lot of through hikersrocking these guys Their lacing system is pretty unique as well as you can tell No complaints on these at all other than the fact that might be just a hair too heavy.

Again these are designed to be more rugged And that ruggedness comeswith an extra ounce or two Luna sandals.

I believe this is the winged Oso Flacomodel I might be pronouncing that wrong Luna was started by ultra runner barefoot Ted from the famous book Born to Run He really emulated that famous tire with lacing-style look These more than anyother sandal on the list are really designed for running People do someserious running in these things Very well designed manufacturing just feelsreally high-quality lacing is durable and smooth just great sandals Luna doesoffer a lot of other models and styles to look at mainly thinner or thickersoles depending on what you prefer different lacing really to help keepyour heel more secure for those runs Unshoes these are the Wokova model verystripped-down model affordable very nice sandals move well with your feet opennice lacing nice flexibility only little gripe is this inner sole area they'vegot these two laces on the outside and one on the inside and it feels just alittle unbalanced like my foots gonna slide out but not a big deal reallygreat sandals recommend them Shamma sandals last but definitely not leastare these Shamma sandals these are the mountain goatsI probably clocked more time and knees than any other pair on the list at leasta year lots of trails lots of everyday use you can see they're finally startingto split a bit they're light but not too light just a great balance very basicno-frills design which I like super comfortable and easy to take off and ononly din might be the tread the grooves are fairly shallow which in myopinion decreases the life of the sole you can see these are pretty slick nowbut again I've worn the heck out of them and then we have Chacos notminimalist sandals I'm not gonna dog on these I really just wanted to add thesein here so you can compare them to the others on the list these weigh about 36ounces the other models are around 12 ounces so these are literally threetimes the weight you can see how the heels are higher in the back then in thefront this is not zero drop with all of the other ones are which is just not mypersonal preference there you have it my thoughts on minimalist sandals let meknow if you have any questions peace.

Crochet Sandals onto Flip Flops | Tutorial Tuesday Ep. 95

hello crafters I hope you're having anawesome Tuesday welcome to this week's tutorial it's Amanda here at craftersautonomous and today I've got a crochet project where we take a normal pair offlip-flops and turn them into these fun sandals a quick word before we jump intothe actual tutorial it I did have some technical difficulties filming thisvideo so there are a couple spots where it gets a little blurry however don'tlet that stop you from watching the videoI barely clearly walked through and talked through all the steps also in thedescription below you can find a written pattern for the steps for crocheting theheel of our project so between the explanations that I give as I'm workingon the project and the description with the pattern you should be able to pieceit together even though a couple spots the focus goes a little bit wonky solet's jump into this project so let's start off by getting our materials I'vegot obviously a pair of flip-flops being repaired that I found a Publix they wereon sale at the end of the season and they're really nice because they've gotthis plasticky firm sole but of course you can just get you know the Walmartkind or a pair from the dollar store that would work totally fine as wellnext we need our yarn I am using some cotton yarn and in particular I'm usingI love this cotton yarn from Hobby Lobby which as a side note I really like thiswas one of my first times using it and I really like this turn I was very happywith it we will need so there's obviously for our tails of yarn but alsoto get this out of here you will need a needle and thread because I feel likehere we're first going to sew around the shoe to create something out we cancrochet in and then of course you need our crochet hook which I will be using aUS size II 3.

5 millimeter hook the first steps are prepping the shoe for me thatinvolves cutting this out you will need to cut out your flip-flop straps if youhave a plastic kind of course you can just cut them and pop the little roundpart off on the bottom but I'm going to clean this up and thencome back once your flip-flop is prepped it is time for my least favorite part ofthis whole process which is the sewing part essentially what we're going to dois we're going to sew loops with thread all the way along and then we will beable to crochet into that so to do that I've got a small needle and you don'twant to go with too big of a neo because there are little puncher holes reallybig and it'll weird the flip-flop down more and I've just got some thread and acoordinating color you can either go for a color that matches your flip-flop baseor one that matches your yarn doesn't really matter I'm going to thread myneedle and I'd like to double it up so we're running two threads through ourtime just for extra strength I'm just gonna pull a big long section of threadnot too long a little get tangle and gonna get harder but long enough so youcan get a good way around the shoe cut my thread and then tie my ends togetherI'll do a couple knots here just basic overhand knots I just had a knot and nowI have a big loop of thread with a needle at the end so I wanted to strikejust arbitrarily along the side by the heel here and for me my flip-flops arenice because they have these holes and I'm going to use those as a guide of howfar is part to space my stitching if you don't have something like that on yourshoe you can go ahead and use a ruler to mark even spacing around but what I'mgoing to do is I'm going to come in just a little ways away from the edge and youleave enough of the sole on the sides that way don't just tear through theside but I'm gonna come through kind of at an angle and I want my name's I'llcome out partway down the side of my shoe see the needle coming through rightthere I'm going to push it all the way through you may want to symbol for thisproject going to pull it all the way to the end and then I'm going to run myneedle through the loop of your and just stuff to secure it in placeand this first one we're going to cinch it up a little bit so the rest of ourstitching though we don't want to cinch it up or else it'll be too tight for usto get our crochet hook underneath so I'm just kind of going along one stitchevery row of these dots I'll go to my next spot come in and come out down theside because I'm saying when I pull this throughI don't want to set you down like that I want to leave it loose about like thatand if you leave it loose it would make your life so much easier when you comethrough and crochet on my first shoe I didn't leave it loose enough and so itwas a lot harder to come under with the crochet hook so we were losing yourloops loose so it's easier to crochet and essentially just going to keep doingthis come from the top and out the side keep almost like a whip stitch where Ijust kind of spirals like that and just keep stitching along the edge so I havethese loops that I can crochet my shoe on I'm gonna work all the way around theshoe and then I will show you how to rupture crochet this project so forreference here as I'm talking about I'm keeping these loops loose you might likea little messy but it will all even out once we start crocheting around now I'veonly got a little ways around the shoe I've got one ways to go but you will getbetter and then we'll get to the fun crocheting part so now I have stitchedall the way around my shoe as you can see we left it fairly loose we willeasily be able to get our crochet hook under there so let's get our crochethook and our yarn and the first step is we're going to just slip stitch along tocreate a border so I like to start by making a slipknot and putting it on myhook and then I'm gonna come to the side and I like to start just kind of in thisinner arch side because I feel like you don't notice it as much when it's allsaid and done also my tail ends of thread I just woke up underneath thestitching and that all get hidden as we crochet around so what I need to do isI'm gonna pick two stitches to start and I'm going to insert my hook under bothstitches and then I'm going to yarn over and work a slip knot now I recommendworking this somewhat loosely as you go around but you do want to stick with asmall hook size so you can easily get under the stitching then I will go to mynext two stitches come under both of them with my hot yarn overand work a slipknot and I will keep working this around going under the nexttwo stitches working a slip knot until I get all the way back to where I startedand then I will do a slip stitch to join you do want to make sure with yourtension though that you leave it loose enough so that way they're not allbunched up they pull a slip stitch through I like to kind of stretch it outa little bit so we can get our hook all the way over to the next stitch so you can start to get a feel for whatwe're doing all the way around our flip-flop edge so at this point I haveslip stitch nearly all the way around if we look right here it's a three-morthread stitching's and i have been working in – but that's okay I will justwork in one for this next stitch and then working – for my last one lastthing I'm going to do is just slip stitch in my very first lip stitch tojoin the round and then once I've slipped stitch them togetherI will fasten off of course we will eventually need to weave in those endsbut won't worry about that later on so now that we have crocheted all the wayaround our shoe the next thing is going to be to add the heel now just a couplequick notes on this I'm gonna size seven and a halfit's flip-flop so that's a size 9 and you may wear a completely different sizeshoe that's okay I'm going to walk you through what I do to make it fit me andI'll kind of tell you how you can adjust it so the first thing we want to do iswe want to find roughly the mill stitch on the heel and I'm going to put astitch counter in it just to make this next part a little easier then I'm goingto count 13 stitches to the side so this is the part what you will adjust it ifyour foot is a little smaller you waive wanted to do say just 11 stitches to theside if your foot a little larger you may want to go up to 15 stitches and youmay need to do the first couple of rows a few times to kind of get a feel forwhat it will look like so you can decide what fit you want but I'm going to count13 away from this so 1 2 3 4 5 6 7 8 9 10 11 12 13 and you want to make sureit's roughly even with your other shoe so they stay balanced that's pretty evenalso if you make adjustments on my basis pattern here you may want to write thosedown so you do the same thing when you make the second shoe but regardlesswe're going to put a slip knot on our hot come to that stitch that's 13 awayfrom the back middle and we're going to insert and just the back loop just thattop loop yarn over and pull up a loop yarn over pull through two and work ourfirst single crochet stitch now I'm going to work a single crochet in thenext 12 stitches out as well working in just that back once I've worked 13 single crochet I'mgoing to work a single crochet increase in this middle stitch that I marked fromthe beginning so again the back loop nicely just means I'm going to work twosingle crochet stitches in this same spot and then the rest of this row isgoing to mirror what we've done so far and we're going to crush single crochet13 stitches so that is the first row for my heel for my second row I'm going tochain 1 and then turn my work and I'm going to work one single crochet in eachof the next 13 stitches and next I'm going to work through both loops of myprevious row then in the next two stitches I'm going to work a singlecrochet increase so two single crochet in this next stitch and two singlecrochet in the following stitch and then to finish the row I will work 13 singlecrochet until I reach the end of the row for rows 3 4 5 & 6 I'm just going totake single crochet evenly along and there will be a total of 30 singlecrochet so let me complete the next four rows and then I'll show you what we dofor rosettes so now that I've worked rows 3 through 6 where I just workedsingle crochet evenly for a total of 30 single crochet we're gonna move on torow 7 so you start by chaining one and turning my work like we do at thebeginning of every row so I'm going to work a single crochet in my first stitchand then I'm going to work a single crochet decrease I do this by insertingmy hook pulling up a loop and second my look in the next stitch point up a loopyarn over and pulling through all three loops then I'm going to work just onesingle crochet in the next 9 spaces then I'm going to work a single crochetincrease in my neck space so one and then two and then I want to work onesingle crochet in my next four stitches and increase nine single crochet a single crochet decrease and a singlecrochet in the last stitch chain one turn your work and now we will begin roweight so again all these rows kind of mirror themselves so this when we startwith a single crochet then we do a decrease work all the way around andthen do a decrease in single crochet at the very end of the row so in our firststitch we work a single crochet then a single crochet decrease and then 24single crochet now I just have three stitches left in the row so I'm going towork a decrease and a single crochet in my very laststitch row nine is going to be really similar obviously we start by chainingone and then turning we're gonna start with a single crochet and then adecrease and then 22 single crochet until we're left with just threestitches in our row and then a decrease and then a single crochet in our laststitch so row ten I will start by chaining one and turn my work in thesingle crochet and our first stitch then a decrease and then I will work fivesingle crochet and then a decrease six single crochet decrease five singlecrochet decrease in a single crochet in our last stitch row eleven I'm justgoing to single crochet across evenly and I have 22 single crochet so now weare on row 12 of course start with a chain one in turn we're gonna start withfive single crochet a decrease eight single crocheting a decrease and then five single crochet tothe end of the row so rows 13 through 15 are going to follow a similar pattern wewill start by chaining one and recognize single crochet in our first stitch thena decrease and then we will single crochet until there's just threestitches left and in those last three stitches we will work a decrease andthen single crochet so we're gonna do is for us 13 14 15 and then fasten off sonow I've worked the heel the last thing I need to do is I'm going to do a singlecrochet border just to kind of round out the edges of everything gonna put slipknot on my hook come down here to the very beginning and I'll go through andI'll go through this stitch along the side and slip stitch it in place righthere and then just along the sides of my rows I'm going to work single crochetstitches so I'm just gonna kind of going along the side try to space them aseasily as you can and just work single crochet stitches try to keep track ofhow many you do on your first shoe so though you can do the same number onyour next shoe but I don't really count as I go along I just kind of singlecrochet along if they're looking kind of bunching like I've got too many I'llspace them out a little further usually I basically just kind of go inbetween every row first I'll put a stitch and every one of these stitchesalong the top here just work a single crochet and then I work right back down the nextside and I will slip stitch it to the next stitch along the edge of our shoealong that base there and then fasten it off so that is the heel of our shoe whatwe have left to do is at this part and add the ties here however I'm playing avery intense game of yarn chicken so I may end up doing my ties in a differentcolor so once move up to this part here so as you may know is I love this a veryflat because I have very flat feet very low-profile feet is what I believe theterm is and of course this cotton the yarn has some stretch to it so if youwant to keep it securely on your foot and you want to do it fairly snug so howmany rows you do is going to depend on how large your feet are but I decided tomake my strap 10 single crochet wide so I'm going to come to this outer side ofmy shoe so if I were working on the right foot I've come to this side sinceI'm working on the left foot I'm coming to this side and I'm going to figure outwhere I want those 10 stitches to be since I've already completed one shoeI'm going to base it off of that and I will put stitch markers where the siteto work so I'm kind of lining it up by the colors here so for me I'm gonna workrolling from here one two three four five six seven eight nine ten and that'show thick my strap will be you of course can make yours wire or narrower justdepending on how you want it to look now I'm essentially going to work abunch of rows of just ten single crochet back and forth so I'm going to put aslip knot on my hook working in just the back loops again I'm going to insert myhook my first stitch pull up a loop yarn over and pull through two to create myfirst single crochet and you can also work over your tails so I'm going towrite ten single crochet until I get to there and then just keep working severalrows so I have matched this shoe to that shoefor me the way I sensed it was I essentially stuck my foot under thereI'll use my hand for illustration pull this side down construction a little bitand thought about how snug and tight that I wanted I wanted it fairly snugbecause like I said I have fairly low profile feet I decided to do twenty tworows of just working ten single crochet back and forth now we do have one lastlittle row to do because if we look at the edge of our shoe here on the insidewe have this extra little triangle piece if you will that doesn't like flat so wecan either attach it and then have it be were feet or we could just crochet inthat shape so the way we're going to do that is we are going to do sixslip stitches and four single crochet stitches now depending on what sureyou're doing depends on whether you do the single crochet or the slip stitchesfirst because it just depends on which way you're facing and you're going onyour shoe on this one we are going to be working up that way so we want to do ourslip stitches here and our single crochet up there we're gonna have mywork facing me so in my very last stitch there I'm going to work a slip stitch back on has my first slip stitch a slipstitch in the next spot for a second one a third slip stitch fourth slip stitch fit slip stitch and six slip stitch andthen in the last four spaces I'm going to work a single crochet so one twothree and four and now all that's left to do is it to attached on this sidebefore I attach it I like to figure out where I'm going to attach my stitchesand I'll kind of compare it to my other shoe again we're gonna haveten stitches to connect to so I like to figure out where those ten would be andMark it just so I can know where exactly I'm working so one two three four fivesix seven eight nine ten and I'm going to slip stitch these together the way Iwanted to do so I'm going to current so my work is like this I'm going to comethrough the back loop that touch the tenth stitch there come through the topof my stitch there and yarn over and pull through everything to work thatslip stitch and sew it through the next stitch along the sole insert through thenext stitch on the sandal strap and slip stitch next stitch in the sole nextstitch on our strap work a slip stitch I'm going to do this along all tenstitches of my sandal strip and across that yarn doesn't actually split thismuch it's just because I'm at an awkward angle crocheting this to get this on thecamera so that's why it looks like this yarn is hard to work with her like Idon't know what I'm doing but I promise I don't normally crochet like this and my last spot here slip stitch ittogether and I like to also slip stitch it to the neck to do a slip stitchthrough the next stitch along the sole just to kind of hold it down reallysecurely and then I'll pull one last big loop through and fasten off so the lastthing we need to do to complete our sandals and obviously we'll need to dealwith weaving in the ends but we also need to make our tie strap now this isall the yarn I have left like this so I'm going to take these ones off and usethis other red color to make my straps this is also I love this cotton yarn byHobby Lobby and quite honestly you can do the straps however you want you coulddo a braid and attach it you could get a piece of ribbon instead of yarn reallyhowever you want to do this I personally like to do my straps with some floatingsingle crochets so that's what these ones over here are they're just floatingsingle crochet stitches excuse me not not floating so crochet foundationsingle crochet stitches if you're not familiar with that I will show you howto do that on this shoe so I'm going to show you how I do it on this side herebut the same process will be done on the other side as well and of course I needto fix this shoe as well we're going to start right here if you're doing thefoundation single crochet tie straps you'll want to start with whateveryou're on you're using and make a slipknot and we are going to put ourhook through the top corner stitch so whatever is the corner stitch of yoursandal put your hook through there and then we'll put the slip knot on our hookside it down and we'll pull that loop through notice first one's gonna be alittle weird and then the rest will get into more the foundation crochet butwhat we're gonna do is in the stitch below insert our hook yarn over pull upa loop yarn over pull through one yarn over pull through to which areessentially the same steps as the foundational crochet but now I'll showyou how we do it when we're working in a previous stitch we're gonna come to thebottom of our previous stitch if you look at the underside is like this Vthere we're gonna go through the bottom of the stitch let's our hook yarn overpull up a loop just through one then we're going to yarn over pull throughone yarn over pull through two I will show you that again in the bottom of thestitch we just completed insert our hook under those two pieces right there yarnover and pull a loop through that stitch yarn over pull the loop through one yarnover pull the loop through two and I have a whole video that explains thisprocess with double crochet stitches I will link it up there in the card butthe same process applies to a single crochet but you can watch that video ifyou want to get a better feel and how to do foundation stitches I'm going to makethese as long as I want so I have enough to tie it around my ankle I'm going todo my tie on this side as well and of course on the other shoe weave it allthe ends and then our shoes will be done hey thank you so much for watching ofcourse if you enjoyed this video let me know and let others know by leaving abig thumbs up also make sure to hit that subscribe button down below somewhereand also hit the little bell icon so you get notified when I post new contentI've got a lot of awesome fall and Halloween and crochet projects coming upso you definitely don't want to miss those I will say that I wore these shoesout and they worked very well and they were pretty comfortable I'm not gonnalie so go ahead and make your own custom crocheted sandals thanksfor watching and happy crafting.

D flip-flop

So in the last video, we built this D latch Which has the enable input as well as the d input and whenever the enable input is high then the output here the Q output is just equal to whatever the d input is and then there's also an Inverted Q output or a complimentary or negative Q output that's always just the opposite of what what q is And then if the enable is not high then it doesn't matter what happens with D input? So this is the D latch I've made a slight Modification from the video from the circuit we had in the last video which is that on the inputs I've added these leds And so if we're not pushing the button then this this is going to be very close to zero volts you know it will sink a little bit of current through the led but not enough to light the led up and then when we push the the button then we're connecting 5 volts to the input and so the input goes [from] [0] volts to 5 volts and then We also have 5 volts that can flow through the led in the [end] this resistor Just limits the current through the led so we don't burn up the led and so I just added these leds so that We can see what the inputs are so to get a better sense of how this works we can look at a timing diagram Which is this here which shows the values of the inputs the enable input and the d input over over time? And so it shows them going high and [low] and we can see We can kind of think through what's going to happen to the Q output And I've left off the the inverted Q output because I think it's just kind of distracting, but in fact I'll remove this led But you know just keep in mind that the you know the d latch it also has an inverted output That's just always going to be the opposite of whatever q is So remember the way this works is whenever the enable input is high The Q output is just going to follow whatever the d input is So just for these periods of time where the enable is high the queue is just going to be what the d is So the queue here is going to be just what the d input is and then the rest of the time when the cute when the The enable is low the Q [output] is just going to stay whatever it is.

So if it starts out off for example It's just going to stay off here.

It's off and so it's just going to stay off and Then he and then here it's just going to stay off and this case is going to stay on and in this case We'll stay off So it doesn't matter you know during these periods what the enable or what the d? Input is doing as long as the enable is off.

It's just going to stay latched where wherever it is So if we want we can [just] verify that this works the way that we did we think it should Yeah, and it looks [like] it works the way we would expect so that's great and hopefully makes sense to you how that works but? often times in more complex digital logic circuits We've got lots and lots of different latches that are latching different values all over the place And it's important to keep all of that in sync and so typically there is a clock of some sort that is that are controlling the Operation of all the different components and keeping everything synchronized And it's important what you want is you want to be able to latch the values at? a particular point in that clock cycle Not necessarily just transparently passing through the values anytime That clock signal is on and so to do this we'll look at a variation of the the latch which is the flip-flop so with the d latch [anytime] it's enabled the input D is going to be output at Q and So if the d input changes while the the latch is enabled, then you'll see a change at the output But oftentimes what's more useful is to think of the instead of having an enable input having a clock input? And then only outputting a change at that Just at the point where the clock transitions from low to high and so this clock is really more of kind of a heartbeat That says at these specific points in time That's when I want the the latch to latch in or change its value and so for example at this point here where the latch? Transitions from low to high that means we want to take this value right here at D And we want that as our output, so that's a high output so if we were already low, then we [would] transition [to] high at that [point] there and Then we want to not do anything so even though the d input changes while the clock is still high We don't care we all we care about is when the next clock pulse is which the next pulse from low to high and then we want to take this value [and] That happens to be high and so in this case the latch won't switch And so it'll stay high here And then we say we don't care about anything that happens even though it goes low, and this is still high here we don't do anything because all we're doing is we're looking for that next transition from low to high [that] next clock pulse and that happens here where d is low and At that point in time, we'll switch [we'll] switch the latch off and then again.

We don't care what happens here.

You know it goes [hi] again.

Whatever, we don't care we're looking for that next clock pulse where it goes from low to high and In that case the d input is high and so at that [time] We will switch the the latch back on [and] in this case.

There's no more transition So we just stay high and so you'll notice [this] is [a] very different Output than we got with with this scenario where we're using the enable But it turns out.

This is actually far more common.

[it's] far more common to want to only switch at a particular instant in time So question is how do we build a circuit that does this? well one way would be is if we could build a circuit that could take this clock input and turn it into Essentially something that would be useful as an enable input for normal D latch So to kind of give an example of what of what I'm talking [about] there is You know imagine we could have we can take this clock signal and get a signal out and put it into some circuit And then get a circuit get a signal out that had these really quick pulses Just at this point where the clock transitions from low to high so if we could build a circuit that could do this then we could use this new signal here at the top as an enable for just the classic D latch that we've been looking at so far and As long as this pulse is is really really narrow then effectively.

We're getting an Instantaneous or or as close to instant aces we can kind of read out of what d is and Transitioning just at that point and so if you look at this, this is kind of like your enable in a regular D latch and then if you have that enable and that d you put that into a regular D latch then this is the output you'll get And hopefully hopefully that makes sense and so you can see if we could somehow take this clock signal and detect these rising edges With a circuit that [we'll] call an edge detector and detect those edges and then and then turn that into a pulse like [this] Then we can build what's called the d flip-flop? Which is a circuit that will take you know that will start with this clock and only transition at these points Where the clock transitions from low to high? So now the question is how can we build an edge detector circuit that you know takes this clock signal and now puts this this? these pulses Well, there's a couple ways to do [it] and one is is this sort of interesting looking circuit here And you might be wondering well, you know what does this do we've got one input and one output and so you know the idea is that somehow a Rising Edge here is going to result in a pulse over here, but you might be wondering well We've got this inverter going into a nand gate [as] we have an input here going through an inverter and You know one side's going through the inverter the other side isn't so if you had you know let's say you had a zero over here Well that's zero you know if you have a zero coming in to zero over here It's going to be a 1 over here, and then you know the and gate and gates going to be a zero It's a you know It's only going to be a 1 if both inputs are ones, and you might wonder well How does how do you get to both inputs being one? I mean if if this is a zero then this is going to be a 1 if this is a 1 then this is going to be a zero because we're inverting this and so this you would think this an gate would never turn on and You'd almost be right, but what happens is if this signal is a zero? you know we have this situation here where we have a zero coming in and A one here into the and gates going to be off, we're gonna have a 0 coming out but when this input transitions from a zero to a one This instead of being a zero is going to be a 1 and Then you would say well Then this would be a zero because we're inverting but the inverter actually takes a small amount of time to switch [States] so when this input changes from zero to one We've got a 1 here immediately But the inverter doesn't switch off for you know a few nanoseconds.

You know very short amount of time but but enough time That for a very brief period of time we've got a 1 and a 1 coming into [the] [damn] gate which turns the end gate on But then of course very quickly the inverter [switches] off this one turns to a zero and now we've got a [one] [in] a [zero] And then of course the and gate turns off, and so it turns off almost immediately But now we have this pulse and we get this pulse [anytime] this input Transitions Low-to-High we'll get a little pulse that comes out, and that's exactly what we what we wanted here in order to detect this rising Edge on this clock signal so that's one way of Building an edge detector, and I would actually encourage you to try building this yourself [there's] a simpler way though that I'm that I'm going to do because you know this is this is going to require [a] nand gate And and you know an inverter potentially multiple inverters you might find if you try to build this you need to stack up three or five of these inverters in a Row just to get enough of a delay so [that] you get a big enough pulse But you know you can give it a try But a much easier way to do it that doesn't require adding more chips here is to use a resistor and a capacitor and so we can use a little circuit like [this] where we go into a capacitor [and] Then you know through through that capacitor, and then we have a resistor here That just goes to that goes to ground And so you're wondering well what what does this do? Well in this case if you've got this the signal that comes in that transitions from low to high like this When it's at zero, we've got you know zero volts across this capacitor and the capacitor is discharged You know because the ground here is going to be at zero.

So you know you've got zero volts over here So that's not not very exciting, but then when it turns on the capacitor Is going to start to charge and as it charges? There's current flowing into it and of course if you've got current flowing through here You're going to have a higher voltage here across this resistor And so as soon as as soon as this turns on this is going to jump up to five volts You know so I mean this is a five volt transition here But very quickly that capacitor is going to charge it's going to charge through this resistor and as the capacitor charges less and less current is going to flow into [it] until The capacitor becomes fully charged and when the capacitor is fully charged then no current is going to going to flow through here And we're going to be back down at zero, and so what happens is this turns on very quickly? And then it slowly or maybe not so slowly depending on on how fast this is but it discharged or excuse me the charges the capacitor charges and so that the voltage over here drops until You know once the capacitor is fully charged you can have five volts on this side zero volts on this side.

[nope] flows and So you can see it is a pretty simple circuit to take you know this rising edge and turn it into a quick pulse Because then this can stay high and this will just this will just be low But you get this nice quick pulse Right at that rising Edge.

Which is which is what we want so question is how how quick is this pulse? And you know I'm not going to go into driving all the math, but you you can calculate the width of this pulse By just multiplying the value of the capacitor and the resistor if you multiply the value of the capacitor and resistor It'll tell you essentially where You know the point or how much time it will take for this capacitor to get about two-thirds of the way charged Which will give you a pretty good sense [of] how? Of how short this gap is So let's build this I've got a resistor [in] a capacitor here.

This is a [0.

1] micro Farad capacitor And then this is a 1k Resistor and so if we want to figure out this this time constant to figure out how how big this pulse is We just multiply these together, but of course we first we've got to get them into standard.

You know Farad's and in homes, so [0.

1] Micro Farad's is going to be 0.

1 times 10 to the minus 6 and Then 1 1 k of course is just 10 to the third and so if we take 0.

1 Times [10] to the minus [6] multiplied by 10 to the third we get 0.

1 times 10 to [the] minus third Which is going to be equal to? 0.

1 Milliseconds because [if] you're multiplying Farad's times kilo Ohms in this sort of circuit you end up with seconds so 0.

1 milliseconds is How long this this gap will be so for our purposes we [can] say that you know K 0.

1 Milliseconds is you know pretty pretty much Instantaneous.

Which is what we're going for here.

We're looking for you know when this clock transitions We just sort of take an Instantaneous read of this d input so as long as in our circuit this [d] is in transitioning anywhere near You know every 0.

1 milliseconds Then we'll be fine and of course in this case.

We've got a button here I'm not pushing it any faster than that, so we'll be fine So let's go ahead and and build this so right now.

I've just got this little jumper here between the enable button and the you know enable part of the circuit so I'm going to take that jumper out and instead We will put this capacitor in So that's this capacitor so from the button We're going to get this pulse And then of course we need this 1k resistor here going to to ground so for the capacitor to charge through So let's give it a try and see if it works the way we would expect And it looks like it works.

Just the way that we would expect it to which is great and you [know] definitely different than different than the the D latch and So that's the d flip-flop and if you look at the d flip-flop? it's basically very similar to the D latch in fact it's Identical except that instead of the enabled you have some sort of pulse detector and in this case I'm using a resistor and capacitor [you] could use this you know this weird and gate inverter thing if you wanted to But something that's going to detect the pulse for that clock pulse and so instead of having an enable input in a d input you have a clock input and a d input and in the Sort of block diagram for that the clock input is usually indicated with a little triangle here that tells you you know That this is in triggered And so that's the d flip-flop, and it's probably the most common way of storing data in a digital logic circuit.

Lecture 31: SR Latch and Introduction to Clocked Flip-Flop

Hello everybody.

We are now in week 7 of this particular course.

We shall begin Sequential Logic Circuit fromtoday’s class.

And we shall have a quick recap of week 6, I believe it was little bit heavy.

Because that was the last week of the combinatorialcircuit discussion, so lot of advanced things were there.

I hope you could assimilate them.

But as we have done in case of combinatorialcircuit – we made a soft start with introduction of basic gates and all.

Then we moved on to build more complex circuits.

So, similarly we shall start softly with basiccomponents of this sequential logic circuit by which we shall make more complex circuitin the a later classes, ok.

So, we discussed a magnitude comparison oftwo numbers, and how outputs like X greater than Y, X is equal to Y, X less than Y wasgenerated – were generated.

And in that case we had two kinds of approach:one is of course by subtraction and another is by comparing the more significant bitsof two numbers successively, ok.

And then we discussed arithmetic logic unit, and we saw that one device which is versatile in nature – depending on the selection unitit does perform one of the many different arithmetic or logic function.

And we saw that how all these devices canbe cascaded and more number of bits can be handled together.

Then we discussed unweighted codes, ok.

And then we saw that how gray code was advantageouswhere two consecutive numbers change by only 1-bit position.

And we also discussed the excess-3 code, wherewe saw that the BCD arithmetic, the way you had conducted before – that can be made simplerby excess-3.

And then we looked at error correction anderror detection codes, and in that context we defined Hamming distance.

And we saw that minimum Hamming distance ina particular coding paradigm; how that can be useful in deciding or in understandinghow many bits can be corrected or how many (error) bits can be detected, ok.

So, in that context we discussed a paritycode, standard parity code – even parity, odd parity code which we discussed in oneof the earlier weeks.

And also we discussed a new code – Hammingcode which can detect 2 error and correct 1 error, correct 1 error in bit position, ok.

So, this is was in brief what we discussedin the – and of course yes, we discussed multiplication and division, right.

And we saw bit you know, seemingly complexcircuit, but we had examples by which we could appreciate how the processing was done throughthe array based structures, in the unit cells, and finally the results were obtained, ok.

So, each of the cases we have defined theunit cell properly and looked at the solution by taking specific examples.

So, with this we start this week’s discussionas I said, we shall start with defining basic units of sequential logic circuit which ismemory element also called flip-flop.

But before that we shall see what is a bistablecircuit.

So, bistable circuit is something where thecircuit is stable in one of the two positions; bi stands for 2, right.

So, both the positions are stable, right.

So, if you look at this you know, a switchwhere you are applying a specific force by hand and all, and then you are connectingthe switch to this particular place.

Then you remove that hand pressure or youknow this whatever force, external force the switch will remain in that position.

But if you again put a force and bring ithere again it will remain there if you do not force it to go to another position.

So, each of these states is stable, ok.

So, in bistable circuit, we can store 1-bitof information.

That that is whether this output is high, Vcc or output is 0, right.

So, together you can store in the contextof binary representation of information, 1-bit information – we can store in the bistablecircuit.

Now moving over to digital circuits.

So, let us see if we have 2 inverters connectedone after another right, and we place a 0 volt here what will happen to it – to theinverter outputs in these cases.

The first will be this 0 volt to the 5 volt, right.

So, logic 0 will become logic over here andagain it gets inverted it is logic 0, ok.

This is understood.

Now while this ground is here you connecta feedback.

So, this feedback is key; this feedback isvery important in developing the basic cell and the sequential logic circuit, right.

In the combinatorial circuit we did not discuss, we did not include feedback.

So, the feedback comes in the sequential logiccircuit discussion.

So, you connect the feedback the way you haveseen from output to the input; why, there is no issue no ambiguity because this is 0volt and this is also 0 volt.

So, this is logic 0, this is also logic 0, this is logic 1.

Now if you remove this ground like this circuitbecomes like this.

What will happen to the circuit? It will remain at this 0 volt, this 0 volthere is driving this one, and this 0 volt is driving this 5 volt 5 volt this 0 volt.

So, it will remain in that place like youknow, as a stable formation right, this output will be 0 volt.

Now instead of this ground if you had startedwith a 5 volt here, then a feedback, ok.

And then you remove that you know, 5 volt;how would have been the output in this case? Output would have been stable 5 volt, ok.

So, this is what we can see a bistable circuitin the context of digital logic representation, right.

But what we find here that this way of youknow, applying external you know, this ground or 5 volt – this is a bit inconvenient.

So, you would look for something which ismore convenient to trigger from one particular state to another.

So towards that, let us look at this circuitwhere we are having instead of NOT gate we are having two NOR gates, ok.

So, you can see the feedback happening here.

And we can write, we can draw the same diagramin a different manner which is you know, cross-coupled, ok.

But there is one feedback you remember andone is in the forward path, but this is the way you can draw it, ok.

And we give these inputs some name S and Rand more about that will be clear very soon, ok.

And this is Q and we shall see that it happensto be the cases, where we are operating it the way we operate it, this V3 will be inverseof V2.

So, this is 0 volt, it will be 5 volt andvice versa.

So, that way we can write it to be Q bar, ok.

But we shall you know, see more of it in thesubsequent discussion, right.

So, consider that both of them are 0 0 ata given time, ok.

So, for a NOR gate 0 is a non-forcing inputok.

For OR and NOR, 1 is the forcing input.

For OR gate if 1 is there output will be 1irrespective of what is there in the other input.

And for NOR gate if 1 is there output willbe 0 irrespective of what is there in the other input.

Isn’t it? So, these are forcing inputs, right.

So, 0 0 is non-forcing input.

So, it will look at what are the other inputsby which the output will be decided.

So, if to start with you consider that thiswas 0, right.

So, then this 0 0 this is 1 right and this1, right is making it 0.

So, this 0 and 1 if the previous value was0, right then it will be 1.

And from the symmetry you can say if thiswas 1 this would, this would have been 0.

So, if you look at this truth table this iswhat you can see; that 0 0 then 0 0 and 1 1.

So, whatever had made the previous value 0or 1 that will be continued with when this two are 0.

So, the prior value of Q it is latched into, ok.

This prior value of Q is latched into, isit ok.

So, this is what we see with 0 0 present.

Now let us see if you present a 0 here anda 1 here, ok.

So, 1 is a forcing input irrespective of whatwere the past values or so, because this is coming from external.

So, this is – this will make it 0 right, andthis 0 0 we will make it 1 even if the previous value was 0 and 1, whatever.

So, ultimately this 1 forces it to be 0.

So, when this is 0 1 right, S is 0 and R is1, irrespective of what is the previous value the output is always 0, right.

And similarly again from symmetry this is1 and this is 0 this is the case, right.

This 1 will force it to be 0, this 0 0 thisis 1.

So, output will be 1, right Q will be 1.

So, this is what you can see, is it all right.

So if it was set, this now stands for – Sstands for set and R stands for reset.

So, when S is 1 and R is 0 we say this particularlatch this is basically – it is called latch because it is latching whenever we are puttinga 0 0 value.

So, whatever the past value which made theQ 0 or 1 because of 0 1 or 1 1, 1 0 that was present, it latches on to the past state;you know, the past value – past state.

So, that is why it is called latch.

So, this S stands for set and a R stands reset.

So, 1 0 is a setting of the latch and a 10 of S and R.

And 0 1 of S and R is resetting of the latch, ok.

Is it fine? Now what would happen if 1 1 was presentedhere? So, the output would have been 0 0 which isfine, I mean as such that is nothing, no ambiguity about it.

But after 1 1 if you try to put into thatresting state when the past value would be latched on to – so, after that if you put0 0 then what happens actually, that this 0 and this is external 0, so both are nownon-forcing, right.

And this 0 is over here.

Now depends I mean, which one of them getsthe 1 before the other.

Ideally one can say that both of them willget 1 you know, together.

So, that 1 will go to the feedback to therespective cases.

So, both 1 will become 0, ok.

So, that is the ideal case (but actually)where the propagation delays are identical – but whatever be the fabrication processor so we will see that one of them – which is not, for sure because of the way it getsfabricated, different transistors and other things are there in the circuit element, passiveelement so, one of them will be having a higher you know, propagation delay than the other.

So, that will respond slower which we cannotsay as a designer which one is you know, going to acquire the 1 value before the other, right.

So, that is something which becomes a bityou know unpredictable.

And a race between these two – who wins andthat is something which we would like to avoid in a SR latch use or application, ok.

So, that is why this 1 1, we are saying asnot allowed, clear.

So, how do we again look into you know, therepresentation part.

So, we will not write all those you know basicgates that we have used, instead we can prefer to put it in the form of a symbol which willhelp us in making bigger circuits, ok.

Otherwise this circuit will become a bit youknow clumsy – too many you know, logic gates and all.

So, when we say SR latch, so this is the waywe can put it.

And if you look at the textbook, two differentsymbols have been used.

In one case Q and Q bar are output – inside.

In both the cases, we will see SR is there, ok.

And that means, this is Q and this is theinvert of it that is what we have seen in the cases; the allowable cases, right.

And, in another representation Q bar – Q andQ bar taken – kept outside, but now there is an inverter, a bubble that is a NOT operation;that opposite operation that is being shown here.

So that means, whatever is the value hereit is opposite here, ok.

So, these are the two conventions we willfind in the textbook.

So, now we can, whatever truth table we hadseen before, now we can put it in a more compact form since we are trying to come up with acompact representation.

So, 0 0, so previous value is retained, previousstate is retained; 0 1 of S and R output is 0; 1 0 output is 1 – state becomes 1 and 11 is not allowed.

So, we had seen the way the NOR latch works.

So, have we – if we had connected you knowNAND gates in the same manner right, so what would have been the corresponding you know, truth table, ok.

So, in the NAND latch if you look at it.

So, NAND – for AND and NAND what is the forcinginput, 0 is the forcing input, ok.

So, if AND gate – 0 is there then irrespectiveof the other input, the output will always be 0.

And for NAND gate if 0 is there output willbe 1 irrespectively of the other input, .

So, in this case if you just look at thisfirst, this particular block, so we will see that if this we are giving it a name S barand R bar because that is the way we see – we shall see that relationship with this particulartable; the previous NOR latch.

So, if both of them are 0 0 right, so theoutput will be become 1 1, right.

And if both of them are 1 1, then it is non-enforcinginput.

So, it depends on the previous value.

So, if the previous value was say 0 and thiswas 1.

So, 0 and 1 this will be 1 and 1 1 it willbe 0.

So, previous value will be retained.

And previous value was 1 and 0.

So, this will go to 1 and 0 – 1 1 it willbecome this 0 it will go to 0 and this will become 1, and 1 will come over here and 11 it will become 0 ok; the other case, right.

You can see it from symmetry also, right.

So, this 1 1 is your previous state, right.

Similarly you can see 1 0 will be output willbe 0, 0 1 will be 1, and 0 0 is 1 1 because is forbidden because after that if 1 1 followsits output becomes unpredictable and depends on the race between this gate and this gate, ok.

Now if we are looking for a SR latch madeout of this and we want a truth table like this so what we need to do; we need to puta NOT gate before it, isn’t it.

So, a NOT gate before it and this NOT gateyou can get by a NAND gate also, by joining the 2 inputs, right.

So, this S bar becomes S here and R bar becomesR here.

So, you can use IC 7400 which has got youknow which is quad 2-input NAND gate to realise this one, fine.

So, this is one IC where within it, the SRlatch is already made, ok.

So, this particular IC if you see there are4 such latch one – IC 74279 – 2, 3, and 4.

So, 1 and 2 – is normal SR latch, ok.

Since it is made of NAND, so you can appreciatethat the input will be S 1 bar it is given a name S 1 and R bar, ok.

And in the other case you have got 2 inputs, S 1 bar and S 2 bar.

So, this is a 3 input NAND gate and this isR bar.

So, for the other gate we have got only oneinput.

And for that we shall have a truth table somethinglike this; how, ok.

So, you can see that if this particular caseall of them are 0 this is forbidden, because then the output will become 1, right.

And then if S 1 is 0 then this output is 1;this output is 1, right irrespective of S 2 is 0 or not because one of the forcing inputhas become 0 for NAND gate.

And at that time if R bar is 1.

So, this R bar is 1 right, just by consideringthe way we had considered it before we can see that this is 1 this R bar is 1, so 1 1it is 0 and 0 is fed back here – it is 1.

So, the output is 1.

Similarly, from symmetry, if S 2 was 0 atirrespective of S 1 the output will be 1.

And when both of them are 1, right; that means, this is non-enforcing and R bar is 0, then the output becomes 0, right.

And when all of them are 1 the output is inthe last state, ok.

So, this is what we can see for IC 74279, where the latch is already there inside the IC we do not need external connection usingNAND gates.

Now, one application of, there will be manyapplications, we shall see later and complex sequential logic circuit will be made.

So right now, we can see one application wherea debounce switch can be made using SR latch, ok.

So, what do we mean by debounce switch? So, when we are basically connecting a mechanicalswitch which is kind of you know having a spring load kind of thing.

So, whenever it is getting connected here, right.

So it will make a connection-disconnection, connection-disconnection, connection and then it will settle, so there will be a small vibration, right.

And when it disengages from here, this isthe output that we are talking about here when it disengages when it is connecting hereit is making a oscillation, but it is connected to 0, so it does not make any difference here.

So, only when it is getting connected at thisplace, getting closed, at that time there is a small vibration because of the you know, spring action that is there.

So, you will see you will see that wheneverit is getting closed for example here, so there is a small vibration taking place.

High-low, high-low it is getting disengagedgetting engaged, right.

When it is getting open and connecting tothis place, so it is a immediate so there is no such issue again it is getting here.

So, while ideal case we want this, but actuallythis is what is happening, clear.

So, this ringing can create issues, becauseit might say that number of you know 0s 1s you know, come into the picture which mightcreate difficulty.

So, it can trigger many events when, actuallyone event has taken place one such closure has taken place, it may count that 1 2 3 suchclosures have taken place.

And each closure might you know, can get countedand lead to certain action going forward, ok.

So, that is something which may be neededto be I mean, avoided in certain application.

So, for that we can use SR latch, right.

So, in the SR latch the switch is – one isS and another is R, right.

So, when it is disengaging from R and connectingto S, so there is a ringing over there, ok.

So, whenever that is happening, so 1 and 0the output is becoming one because it is getting set after that when it is getting, S becauseof the ringing, so it is becoming 0.

So, this is a 0.

So, previous state is retained, ok.

So, there is no issue with that, is it clear.

Similarly when it is coming to when it isgetting disengaged from S and coming to R right, it is getting disengaged no issue, but when it is connecting to R there is a small vibration.

So, R is becoming 1 0 1 0 for sometime.

So, whenever R becomes 1 for the first placeand this is 0 right, so it will get reset; so it has got reset.

After that during ringing this is – this remains0 and this is 0.

So, 0 0 means previous state is retained, ok.

So, if you now take output from here, therewill be no effect of bounce.

So, effectively we have got a debounce switch.

Now, we move little bit further, ok.

We look at further use of latch, the basiclatch by introducing an enable input, ok.

So, this is the basic SR latch which couldbe made up of NOR or NAND, as the case might be, ok.

So, that is – that part we shall see moreyou know, elaborate circuit later.

So, what we are doing here that we are putting, we are making SR go there through two AND gates like this, which has got an enable input.

So, when enable is 0 so these two outputsare 0.

So that means previous state is retained, ok.

So, this is the case – no change.

And when enable is 1, when enable is 1 andthat time depending on whatever we is this SR value this 1 1 is forbidden of course, the normal action takes place; is it clear.

So, we are not allowing the SR input to affectthe final output at any time – at all the time.

We are only allowing it when it is enabled, ok.

It is like strobe or you know, the kind ofthing that we had used before; for multiplexer, demultiplexer those circuits if you remember, ok.

So, the circuit, this circuit is acting onlywhen or made to work only when enable is at 1, ok.

So, what is its implication? So, if will look at a timing diagram, right.

So, you can see that when enable is at 0 likethis place, this place, this place, this place, right whatever changes are there it does notactually I mean, the Q will remain at that value in those cases.

So, t1 – t2 is the window in which any changecan be accommodated.

So, S was 1 and R was 0, and the Q was 0, so that makes I mean, if enable was not there whenever this S and R; S was 1 and R was 0- the Q would have been 1.

But the enable comes over here only here atthis point at t1.

So, at that time only Q will go to 1, right.

Now t1 to t2 there is no change in S and R.

So, Q remains at 1 at t2, at this point t2 after that enable is 0.

So, after that R becomes 1 and S becomes 0at some point of time over here.

But that effect does not get reflected inthe output Q – why? Because enable is at low, right.

So, again it gets trigger; again it gets theenable signal over here at t3.

At that time, it sees – it finds what is thevalue of S and R at that time.

So, S is 0 and R is 1.

So, that time it will go to – it will becomereset.

So, in between before the enable was thereif S and R had changed their value, it would not be captured by the final output, right.

So, only when the enable is there whateveris the value of S and R that gets transmitted and reflected in the final output.

So, this is the idea, ok.

So, whenever we want the SR flip-flop to workwe put the enable, otherwise we allow the S and R input to settle if there is any transientand all.

We do not want the final output gets you know, changed before S and R are you know, properly settled.

So, enable is giving that you know option- period for the inputs to get settled.

And this gives rise to what we end with today’sdiscussion – is called clocked SR flip-flop, ok.

So, the sequential circuit that we shall discussit is called – it will be actually synchronous sequential circuits.

So, most of the sequential circuit are synchronoussequential circuit, where the state change takes place synchronous with an external clock, ok.

So, this external clock actually totally decideshow the these different the sequential operation of the different kind of elements inside thecircuit, ok.

So, this particular clock would have you knowa waveform something like this right, so it goes high and low and all.

So, this is one clock cycle, right and ineach clock cycle you are looking for one state change if it is so desired by the input tothat particular bistable circuit.

In this case, this particular SR latch thatwe have discussed, ok.

And usually latch with a clock is called aflip-flop, ok.

But then you will see that in the text itis says latched SR flip-flop.

So, basically latch type is SR flip-flop.

So, basically they are referring to latchSR flip-flop, but in other text, generally speaking, presence of clock – flip-flop meansa presence of a clock, and latch means it is just the last stage of where the memorypart is there, where the value is latched into, ok.

So, that is the way distinction is often madein this particular field, .

So, then how this clocked SR flip-flop wouldlook like.

So, in place of now enable we are puttingthe clock, ok.

So, whenever the clock is high, right.

So, the input, change in the input can bethis S and R can be reflected in the output, ok.

So, in this case for SR flip-flop, this isa SR latch right, and this is the AND gate and this was enable as before.

So, we have put the clock over there, right.

And for NAND based circuit we remember thatthis was a NOT gate, right one 2-input NAND gate were put together to get S and R otherwisethis was S bar and R bar, right.

So, we can now use the other input of theNAND gate to put the clock, ok.

And we can see the clock is 0 this outputwill be 1 1, these are the forcing input for the NAND gate.

So, 1 1 means, right a for a NAND gate 1 1means previous state will be retained because that this is non-enforcing input for the NANDgate.

And only when it is 1, so this is now non-enforcing.

So, based on S and R the value will be transmittedhere and accordingly the final value will be arrived at, ok.

So, this is the basic SR clocked flip-flopcircuit.

And the symbol for this is this – the onethat you see here.

And this is also called level triggered flip-flop, because we’ll see edge triggered flip-flop in the next class.

So, level triggered flip flip-flop means wheneverclock is at a particular level.

So, that time it is allowed to trigger, allowedto change the state, ok.

And if we had put an inverter over here, aNOT gate over there, then the change would have been in this stages of the clock whenthe clock is low; isn’t it.

So, at that time would have said that, ifthis is positive level triggered high level triggered, so that would have been negativeor low level triggered, and at the time there would have been a bubble sign over here, ok.

That is a difference.

Is it clear?.

So, with this we conclude today’s class.

A bistable circuit has two stable states.

To summarize – its value changes only by externaltrigger.

SR latch – 0 0 is the input when the previousstate is latched into, 1 1 is not allowed.

And we can get bounce-free switch out of ordinaryswitches using SR latch.

And in gated SR latch or clocked SR latchthere is additional input which enables SR input to go – pass through, make changes inthe final output.

And in synchronous sequential circuit thisclock is very important and one state change we are looking in every clock cycle, synchronizedwith the clock, ok.

Thank you.