Hey guys, it's Nate, aka the Foot Accountant. Welcome back to the channel. We got the 85 times 5, but we need more. EA Sports, it is July. We just need more content when the quality is just not as good as it has been in the past couple of weeks. It seems like EA has kind of lowered the quality meter in the past couple of days in this game, and I want to talk about that a little bit, but there's still a lot to do on this game with eight more Summer Swaps tokens dropped yesterday. We do have player picks now that are repeatable. It's the 81 plus, not the 82 plus, which is cheaper, but I think the 82 plus was a little bit better. We're still going to be doing a lot of these this week, so I want to take a look at all that and of course just kind of look at the market in general with cards actually going up on weeks and times like these where we don't see content being that crazy, right? Especially over the past two days, you've got some of your cards from the mini release from Shapeshift, there's Team 3 actually going up a bit, and across the whole market, meta cards out of packs have risen a little bit because the content is just not super crazy, and a lot of people are now just, I think it feels like a lot of people are just waiting for Friday because Friday is the huge Summer Swaps token reward day. So I want to take a look at all that, and we do have one leaked SBC maybe coming today on Tuesday. We'll talk all that more in today's video. If you're excited for it, hit the thumbs up and of course, subscribe if you're new. Let's start with the top from the top and talk about this 85 times 5 because yesterday I said, hey, guys, there might be potential this dropping. EA did end up dropping the SBC. We can do it one time every single day. It looks like, as you can see here, repeatable every 24 hours, 12 to go until we can do it again, at least for when I'm recording this. It's not like that expensive, but I also don't think that it's that great of value, especially with, again, another requirement for a team of the week or a team of the season player making this SBC a little bit extra expensive and again, 90,000 coins. Here's the problem with this SBC just from a value standpoint. 90,000 coins to get this done. Everybody loves this sort of gamble SBC, but when you have 85 ratings being 8,000 coins you're like, Nate, I'm going to pay 90,000 coins to have a chance at packing, you know, 5, 85s or at least 4, 85s which are worth 8 to 9,000 coins a piece. Most times doing this pack, you're really not going to make your money back. If it was an 85 times 10 at this price, that'd be great and I think everybody had great expectations including myself for the 85 times 5 but the reality is it's just not going to be that good right now for a couple different reasons. Reason number one is think about how many cards we have in packs. This is the biggest reason of the two. Number one, we have so few cards in packs to win what we were used to as the 85 times 10 SBCs in the past couple years in the summer when that SBC is really hyped and so many people are excited to do it. There are only 11 cards in packs right now. It's not like the pack weight is super insane. I guess there's the mini release that is out as well, so it's 11 plus 3, so 14 but it just seems like the pack weight on the weekend was pretty solid from the upgrade packs and from the lightning rounds and stuff like that but there's not that many cards in packs for what we need for an 85 times 5 or an 85 times 10 to be insanely overpowered. We need all of those re-releases, those batches. We remember last year during footies and summer stars where they would re-release old special cards in packs. That is the type of pack content in packs cards. There needs to be a lot of in packs promo cards, either team of the weeks, you know, team of the seasons, past promos. When those sorts of cards start getting re-released into packs, that's when an SBC like this is really, really going to shine. It's just that first reason again is there's just not that many cards in packs and the pack weight is just not there because of it. I saw so many people opening these SBCs yesterday and like not even getting promo cards, right? So many people are just getting gold. You know, you're getting some good walkouts, some pretty good fodder. If you can snag a 90 rated card, you know, like it's a Stagon or a Harry Kane or a Conte, then it's kind of worth it.  Then in the back of the pack, you see that there's a shapeshifter hero. So that's kind of the biggest thing. Again, the pack weight is just not going to be there. And again, number two, we just had way too high of expectations, right? We had way too high of expectations for a pack that can only be half as good as the 85 times 10. I myself got a little over excited for this, I think, just because again, everybody remembers the 85 times 10 and it just can't be that good when it's only five players. And again, like I said, less cards in packs at the moment. So that's kind of the problem with the 85 times 5. Now, am I still going to do this every day? Yes, I am. But here's the question I want to pose right now. Could it actually be worth it? This is like if you have a lot of coins and you're going to be grinding through all the menu content and get all this done. If you don't have a lot of coins, I'd be very, very careful with this gamble upgrade right here.  But is it a play to actually save and not open this 85 times 5 right now and save it maybe a week? If this Friday, they start re-releasing past cards and packs like past specials and promos. I don't know what this Friday is going to bring but if they do something like that either this week or next week, it might be worth saving this pack for a few days for a little while. Stack these up and just wait to open them until you either need the fodder for some sort of SBC that you want to do or wait until they start re-releasing promo cards and packs if it's very soon. That, you know, time to save your pack ratio, if you will, might be worth it. It just kind of depends on what you're doing. It's also July, so if you're like, Nate, I just want to open the pack and hope to pack somebody cool, then I completely get that. But it might be worth saving some of those packs because right now, they just don't seem to be that hype. Although, yes, there are some cool cards and packs. I'm going to open mine today on stream on Tuesday. Excited to get back on the stream crime. Missed it in the last few days with a crazy busy weekend moving and all that good stuff. But I'm also going to keep grinding the 81 plus player picks. I know a lot of people are like, man, there's nothing to do right now. I disagree with saying that there is nothing to do. But I do agree with the fact that saying, okay, EA, we would like a little bit more content in this type of time of the year to keep us engaged. I think I do agree with that just a little bit. Now, I've got five player picks here because I haven't opened any yet. And I just want to see how these are. I put them together from the club. 81 plus player picks. I would have loved the 82, like I said. You're going to still going to get some pretty good cards out of here. You see me get a walkout, the Bala and the second one. Of course, only nine players is very nice when you have less players require of this SBC. Except it doesn't make sense. They require 40 chemistry for this. But the 82 plus player pick last week, I believe only required 30 chemistry. So that doesn't really make sense. But of course, these are hit or miss as they always are. One walkout every five and 84 is not too terrible because they are kind of cheap. I'm going to be doing a bunch of those this week just because why not? Trying to get a lot of those crafted and at least do a lot of those to get fodder to complete upgrade SBCs. Like I said, I'm going to save my 85 times five. Now, will we get another sort of upgrade pack today on Tuesday? That's the question because they're re-releasing the 85 five every day. And it's not like it's a... This kind of reminds me of like Team of the Season Ultimate where we had the eFix Tots and the Tots upgrade pack like every day. That was like good content, right? That was really high level, very engaging. There were Tots cards and packs and it was a great time to be releasing Tots card SBCs like that. If they were putting out like an eFix Tots or like a 93 plus Tots upgrade like right now every single day along with this, that would be fantastic. But as of right now, that's the kind of like next step up of content that we are needing. We're going to be able to do this again today. Again, open it or save it, whatever you want to do or craft it. You can even try to craft this with 81 plus upgrades but we really need some sort of like other upgrade pack today on Tuesday to make, you know, bring a little bit of height back to the game. Now, the other thing that we have that could be dropping today and I know I'm covering this a little early but we have one leaked SBC player and that is it, Martinez Corta. His base card is a non-rear gold center back in the game. Now, I have no idea what this guy is going to get position change to. It's going to be a midfielder. If he is going to be a striker, a right wing, left wing. We've seen center backs go to striker. We've seen center backs go to right wing with St. Jude's Day. No idea what this card is going to be positioned as but he is our only leaked card that we have at the moment. Since we didn't have a player SBC yesterday besides the icon Garencia, I do imagine that it's possible that we could get this player SBC today alongside of some other new upgrade pack and that's probably going to be our Tuesday content for today on the game. Again, I'm really curious to see what this card is. It might offer some pretty interesting links with the Argentinian links in the Serie A but we'll just have to see what kind of progresses through with that. Now, speaking of the content that dropped yesterday as well, Garencia, I just want to cover this really fast. His card, of course, as you would expect, has dropped a lot in price. He is 700,000 coins, just bounced back up slightly. He was 900k before everything happened yesterday. His SBC is not coming at the most favorable price, though. 788,000 coins, as I refreshed the page and his card is like 100,000 coins cheaper on the market and also at this time, we have the best right mid in the game, Gareth Bale, that is what everybody wants for their team. So, you know, a Garencia card, not bad but if you're doing like all the gamble icon upgrade packs, it's probably a guy that you've seen pop up from one of those icon moments upgrades.  I just think the value is okay, though. It's not great. It is just okay. Now, speaking of values, let's talk market here for a second. Actually, before we do that, let's take a look at the objective swap tokens because we also mentioned this in yesterday's video saying, hey, EA dropped eight tokens last week. Could they do it again? And they did. So now we're feeling like EA is very ahead on the tokens after they dropped, like we mentioned, another set of eight. So now we are at 25 total swap tokens for summer swaps two after the ones that they dropped yesterday. Two more squad, we're sorry, four squad battles games for Portugal and MLS and then Serie A and La Liga in the friendly modes. You win four matches and then you get yourself a player pick and two swap tokens per. This is a very nice grind. So again, a lot of people are like, Nate, there's nothing to do right now in this game. I disagree because you do have a lot of gameplay to grind to get yourself swap tokens, 16 swap tokens available here in between these two objectives. So very nice. And I'm hoping to get these done by Friday because Friday is the huge day. Again, I'm going to keep talking about it like every single day. Friday is the day that the summer swaps tokens will be redeemable and we're going to be able to turn in all of these cards for something sick on Friday. And now that we have 25 tokens released, I would imagine that by the time we get to Friday, we're probably going to have somewhere between 28 and 32 tokens released. And that's going to mean that people are going to be able to claim some of the biggest and best rewards that are out there from summer swaps. If you think about it, right? We got like the, I think it's 30 tokens for the, what is it, 96 plus TOTS, EFIG's player pick, like that big player pick. Some people, myself, almost included, might be completely done with summer swap tokens on the time that we hit Friday because if I'm able to get somewhere around like 20 to 25 tokens, I'm going to take all the fodder packs and one of the player picks and be close to done and maybe just grind some other ones throughout the second half of the swap tokens before we hit to 50 and everything. But a lot of people are going to be taking a lot of packs and a lot of really cool player picks this Friday. So this Friday is going to be very, very hyped because of that and because of how many tokens have been released. So that's what I'd be grinding this week if I were you guys. You're like, Nate, what do I put time to in the game this week? Get those objectives done. Get those games done or get those SBCs done as we continue to probably have a couple, you know, shapeshifter challenge SBCs this week and we'll give out those summer swap tokens. So I would definitely grind that this week. And again, grinding player picks, right?  Unless you don't have a lot of coins and you want to save them, I completely understand that. Then maybe you don't do that there. But speaking about coins, speaking about values on the market, let's take a look at these shapeshifters because like I mentioned, with the content yesterday, not being that crazy, right? 85 times five, cool. But not that crazy of content. You have seen some of these cards rise further in price. Valverde is over 900,000 coins by a decent amount now. And a lot of your shapeshifters from Team 3 did bump up in price yesterday, specifically your most meta ones. Leroy Sane was like $270,000 to $280,000. He's now over 300,000 coins. Ribbet Rhee is back up a little bit. Rashford's up like $100,000. The Valverde, of course. Like I mentioned in last night's video, I said, hey, probably some of your Real Madrid links are going to continue to rise. I still have Marcelo. Marcelo won even further. He was like 4 million coins flat. He's now 4.3. Modric went even higher yesterday on Monday, going over 300,000 coins. You can see he started at $280,000 and then kept going over 300,000. As people are just going out, they're crafting that Gareth Bale and they're buying cards to link up together in their squad. So specifically those Real Madrid and some of those La Liga links continue to rise as this is the biggest card still in the game at the moment right now. So that's what everybody's kind of grinding towards. And I feel like EA's letting us breathe a little bit this week, dropping a lot of tokens, dropping a little bit less content, trying to allow us to get all of our swaps done and completed, maybe grind a couple of upgrade packs and keep the content a little lighter this week before they hit its hard probably on Friday with who knows what else we're going to get besides the summer swap rewards being released. But that's also kind of asking the question at the moment, like is the shapeshifter's promo like is the hype dying for these cards? Team 3 is just not as good as the first couple teams in terms of the packability for a lot of these cards. Yes, the hero shapeshifters are pretty cool, but for most people they're like, you know, nothing's super special and it's nothing that they want to really, you know, go out and grind too much for. I think that's the problem with the hero shapeshifters is they look good, but they don't look like super insane and all of them except for Ginola and who's the other one? Ginola I think is the only one that is actually worth something. I guess you could include Ole in that list as well, but the whole entire rest of the hero shapeshifters are like 110K and below. Gomez is 100,000 coins. The one that we had on Coler, where's Coler? He's 100,000 coins as well. So so many of these guys are just dirt cheap like the rest of the shapeshifters team 3 is. Again, apart for our couple cards up top, it just kind of gives you that vibe that EA wants things to be quiet this weekend. What do we know about times when they do this?  They bring it back huge, right?  This promo is dying. EA sports, what are you doing? Give us more stuff. They always come back and hit us with something huge. Not too long after a time period like this happened. So it's times like this where we got to stick it out, grind your summer swaps, get a little excited about some player picks. They're still going to be dropping upgrade packs this week, some gamble packs. If you want to get involved with those, just be careful with your coins. There's still a lot of content to come. So that's kind of what I would say. Just weather the storm right now of the slow content. And pretty soon, basically by the time we get to this Friday, it's going to kind of turn back around again with the summer swaps rewards and whatever else they bring out on the game happening this Friday. So yeah, that's just kind of the vibe of the menus right now, really. I'm going to try out some of the shapeships of their cards today. I'm excited to kind of look at those.  I would like to get Ole done. And Trent, I want to get done as well. There's plenty of SBCs right now to craft, which is very, very nice for the 81 plus player pick being there and being available. And got a lot of player SBCs to do with the fodder that we get from that. And honestly, guys, that's kind of the video for today. I know that it's just not that high of a time. I'm with you. I feel that. We were hoping for a little bit more so far with this week of the Shakespeare's promo. But it's not over yet. Hopefully EA hit us with something sick today. Good luck if you're doing the 85 times five again. It's still a fun pack to open. Don't get me wrong. I know I'm just kind of slandering the name of that pack because the pack weight's not that great on it. But it's still a really good pack. There's still potential to pack a lot of players. And if you're not feeling it, then just save it. You'll be happy two or three weeks down the line. Max, when they start re-releasing promo cards and packs and you open one of these up and you get like three special cards in it that are all 88 plus, then it's going to feel like it was worth your time and your value and the weighting maybe, right? But of course it's a pack. So you could open it in three weeks and still get 385s and that would suck. So, you know, that's kind of the vibe of the game at the moment, guys. I do want to know in the comments down below what are you doing right now in the game? What are you enjoying? Are you enjoying the objective grind? Collecting your swap tokens? Are you logging on every day? Checking the content? And then like, nah, fam, I'm out. Or what is it for you that is still keeping you at least watching some FIFA content and somewhat interested and intrigued with FIFA 22 in July? Let me know down in the comments what has got you still going on this game. Because at the bottom line, there also is a lot of great cards to try out and I totally understand people that just want to try out fun cards. Maybe an MLS fan bringing Eugenberg to MLS is really hype. Ribeirri might bring somebody back as a card that they really want to use. Gomez, Valverde, Rashford, Ginola. Georena makes me want to play with a USA team, right? It's that sort of stuff that EA does a great job with keeping us involved with the great cards that they put on the game. So maybe that's bringing some of you guys back as well. Again, let me know down in the comments. But if you did enjoy today's video, hit a thumbs up on it and, of course, subscribe if you are new. It's been Nate the Foot Account and I'll catch you guys later. Peace. Out.


Welcome back to Tennis Talk, my name's Cam Williams, and we have a big event this week, an ATP 500 event. The Vienna Open. It's a big event with a lot of big name playing. Towards the end of the season, players looking to get into form before the ATB finals, and of course the Davis Cup is happening at the end of the year as well. So a lot of players looking for some form. We haven't got the defending champion Ruebler, but we do have a lot of big names playing. Let's start at the top of the draw. So starting at the top of the draw, and Stefano Siddi pass. He plays Grigory Dimitrov in the first round. That is a crazy first round matchup. The number one seed versus Dimitrov, who's in great form, circled that one as one to watch. That is a dangerous match for Siddi pass. Winner of that match takes on either Lyovic or a qualifier in the second round. Then we've got Montfiest versus Moussetti. Winner of that match takes on either Fanini or the number eight seed Schwarzman in the second round. So another blockbuster first round matchup. It's a crazy, crazy tournament. Then we've got the number four seed Rude. He takes on Harris in the first round. That is a tough matchup for Rude. Very, very tough. Harris in good form. Winner of that match takes on either Sonego or Garin in the second round. Then we've got the wild card Dennis Novak taking on a qualifier. Winner of that match takes on either Opelka or the number seven seed Sinner. So all the seeds in the first round here are getting terrible matchups. Very tough. We could see a lot of upsets in this event with Sinner taking on Opelka. That is dangerous for Sinner. So the players to watch out for, you've got to watch out for the big seeds. Siddi pass and Rude, both playing the A-3 Finals at this stage. You think Rude would probably qualify with a couple more wins. And Siddi pass is already qualified. But you've got to keep an eye on Sinner as well. A lot on the line for him this week. He is in contention of making the A-3 Finals. But it's got a very tough first round with Opelka. Doesn't have a good draw. So we'll see what happens. But a lot on the line, especially for guys like Sinner and Rude, who have still yet to qualify for the A-3 Finals. Sinner especially needs a big week this week. Going to the bottom half of the draw now and another blockbuster. The number five seed Hercatch taking on Murray in the first round. Another match you've got to watch in that first round. Nightmare for Hercatch. The winner of that match takes on either Elcarez or Evans in the second round. Then we've got Basilash Vili taking on Karina Busta. Winner of that match takes on either a qualifier or Baratini in the second round. Then we've got Ojalia Seem, the number six seed taking on Berenkis. Winner of that match takes on either Nori, the Indian Wells champion, who's unseeded, taking on Fuchovic in the first round. See how that one plays out. Then we've got Diminor taking on a qualifier. Winner of that match takes on either Krajanovic or the number two seed Veraev in the second round. And that is another tough matchup for a seed in this one. Super, super dangerous draw. Players to watch out for. You've got to watch out for Zverev and Baratini. Both have already qualified for the A2B finals. So at this stage, they're just looking for some form going into the final weeks of the season. Definitely got to keep an eye on Hercatch. He could be playing in Turin at the A2B finals if he has a good week here, but he's got to get through Murray in that first round. That's a nightmare. And you've got to keep an eye on Nori because Cam Nori is also in contention after winning Indian Wells last week. He is in contention of making the A2B finals as well and being unseeded. Man, what a draw. This has absolutely stacked this draw with the unseeded players could easily win this event. I mean, anybody could win this event as we saw at Indian Wells. And this is a very similar draw to that. So a lot of the line for a lot of players, especially for those ATP final spots are near couple left. So there you have it.  Absolutely stacked. Anybody could win this. Like I said, you've got players like Nori who are unseeded. I think Basilash Vili who made the final of Indian Wells, he's unseeded. All the top seeds are having bad first rounds. You've got Murray playing her catch. You've got Vanini versus Schwartzman. You've got Sidney Pass to meet Rob. I mean, it's just going to be a nightmare for the seeds in this one. Let me know down in the comments below. Who do you think's going to win? Because I have no idea who is going to win this one. It could be anybody. It could be Sidney Pass. It could be someone who's unseeded. Let me know down in the comments below who do you think's going to win? So having a look at the draw and I'm going to go with Beratini to win this one just because he's not playing against a very tough opponent in the first round. He could be getting a second round opponent that's very tough, but he's playing a qualifier in the first round and that's the only reason I'm picking him because he's got the easiest first round out of everybody that is seeded. So I'm going to go with Beratini to win this one but again, anybody could win this. Who knows? It could be an unseeded player. It could be a qualifier. Who knows? Again, let me know down in the comments below who do you think's going to win? So the Vienna are open. It's a stacked event and no seed is safe.


My name is Cole Swiston, a fourth year medical student at the University of Wisconsin School of Medicine and Public Health, and this is a brief video on evaluation of the red reflex in adult and pediatric patients. The objectives for this video are to understand the basic physics and physiology which result in the red reflex, to learn the purpose of red reflex testing in both pediatric and adult patients, to learn how to perform red reflex testing with the direct ophthalmoscope, to see our other video on the use of the direct ophthalmoscope for more details. Finally, become familiar with basic etiologies of an abnormal red reflex in both pediatric and adult patients. The red reflex is a reflective phenomenon seen when light passes through the pupil and is reflected back off of the retina to a viewing aperture, creating a reddish-orange glow. You may notice this commonly in pictures with flash. Red reflex testing is a valuable tool for detection of abnormalities in the normally transparent visual axis or in the retina. Loss of transparency in any of these structures can alter the red reflex, including from front to back, the tear film, cornea, aqueous humor, lens, vitreous gel, and retina. In pediatric patients, abnormalities in the red reflex can be the first clue to sight-threatening conditions that cause amblyopia or life-threatening pathologies such as retinoblastoma. Similarly, the red reflex can assist in the diagnosis of conditions causing visual loss in adults. When examining the red reflex, look first for its presence or absence, the color of the reflex, brightness, and, importantly, symmetry between eyes. In order to perform red reflex testing, position your patient so your eyes are level with theirs and dim the room lights for better visualization of the reflex. In this case, we'll leave the lights on so you can see the technique. So now we're going to position the patient so his eyes are level with mine. Take your direct ophthalmoscope, switch the on switch to the on position, and set the diopter setting to zero or to match your refractive error. Position the direct ophthalmoscope close to your dominant eye and then 12 to 18 inches away from the patient's eye. Direct the light source towards their eye and have them look towards the light. In a pediatric patient, it might be helpful to use hand motions or toys. Position yourself 12 to 18 inches away from the patient's eye and direct them to look into your light. Shine the light on each eye individually and then both eyes simultaneously to check for symmetry of the reflex. This image illustrates a normal red reflex with a reddish-orange glow. There is no dulling or whitening of the reflex, which indicates a transparent and healthy visual axis and retina. Also note the symmetry between each eye. The American Academy of Pediatrics recommends red reflex testing in all patients during the neonatal period and during all subsequent well child and routine health appointments. Any abnormalities discovered, especially leukocorea, require urgent referral to an ophthalmologist. Leukocorea is a term for whitening of the red reflex. The most common conditions causing this whitening are retinoblastoma, a serious tumor in the back of the eye, cataracts, persistent fetal vasculature, or Coates disease. Coates disease is characterized by abnormal blood vessel development in the retina and can threaten vision if left untreated. Another important aspect of red reflex testing is the evaluation for symmetry between eyes. Asymmetry would be considered an abnormal result and is generally evaluated with the Breckner test, where both eyes are visualized simultaneously with the dracked ophthalmoscope. In the trabismus or misalignment of the two eyes, the deviated eye will generally have a lighter and brighter red reflex. If the refractive error is different between the two eyes, termed anisomatropia, one reflection also may be brighter than the other. It is especially important to evaluate for these conditions as they both may lead to amblyopia, which is abnormal development of the normal visual pathways. Similar to a pediatric patient, dulling, dimming, or asymmetry in an adult patient often indicates opacity of structures in the visual axis. The most common cause of this dulling in adult patient is a cataract, but may also clue you into other pathologies in the cornea, vitreous, or retina. We hope this video helps you become more familiar with the basics of red reflex testing. Thank you very much and be sure to browse the many other videos on the Moran Core website for additional information on core ophthalmologics, knowledge, and skills.


So, welcome to the fourth lecture of digital system design with PLDs and FPGAs. Before continuing I will run through the previous lectures slides to be in sync, so let us move on. In the last lecture we have seen the synchronous sequential circuit, its structure, the design and we will see the, we will do the timing analysis today. But quickly we said that the synchronous counter is the simplest synchronous sequential circuit we can learn. So, we try to build everything you know starting with the synchronous counter, so suppose we have taken an example of a mod 6 counter which counts sequentially from 0 to 5 and back to 0 and so on. So, we said that you need for binary encoding 3 flip flops because logarithm of 6 to the base 2 is 2 point something and so we take the integral number of flip flops 3 and I also said that we will not show individual flip flops we will show it together because we are trying to build complex system. So, all the clocks are tied together when the reset comes this is 0 that is all we have now in the next clock head you have to have the 1 and the next clock head you have to have the 2. So, the idea is to decode the next count from the present count, so we put a combinational circuit here before the flip flops or registers and take the present count and try to decode the next count so that when the clock comes the next count becomes the present count and we call it present state of the counter and this is the next state which becomes the present state upon the clock and this combinational circuit has to be designed and that we know that we have to design the truth table we have to write the truth table. So, to be able to design that and we write the truth table in terms of input as Q2 Q1 Q0 D2 D1 D0 then form 3 equations for D2 D1 and D0, so you get Di as Fi of Q2 Q1 Q0 i is 0 1 and 2, so we say next state is a function of the present state and you should know that basically all the intelligence or the computation is in this combinational circuit. The flip flop just holds it, store it for it to work at the precise edge you know when the clock comes this is let in okay that is the function of the registers it serves as a memory to hold and the precise timing is achieved by the clock, so everything is in synchronous with the clock. The state of the count change in synchronous with the clock that is why it is called synchronous counter and we said suppose you want to design a mode 6 counter which does not count in this sequence the sequence may be different it is not in order but like the sequence could be 0 5 3 2 1 4 0 and back and that case it is simple you do not do anything you change the truth table to reflect this sequence then you get that counter, so that is very simple and we have looked at the output waveform, so the count changes upon the clock but not immediately there is a clock to output delay of the flip flop and we know that there are you know this shows the multiple bit 3 bits and there are 3 delays for Q2 Q1 Q0, so we represent the worst case delay and you should also know that many a times this transition is not that it will transit smoothly from 1 to 2 because 1 is represented as 001 and 2 is represented as 010 in between there could be transitory state in this case there could be a state 3 for a brief duration here I have not shown that but normally when you simulate a circuit you will be able to see that for ease of drawing I have not shown and it is very difficult to say practically whether it will happen or not it might happen sometime you will see when it happens okay. And I also reminded you last time saying that when we abstract to the next higher level do not lose sight of the detailed diagram, so we are showing the 3 flip flops together everything together but you should know that these are 3 flip flops are separate the D0 is a function of in this case only Q0 but in general case D0 can be a function of Q2 Q1 Q0 again same D2 D2 and D1 could be a function of Q2 Q1 Q0. So there are different circuit like you have a D0 there is one inverter which is one level but when it comes to D1 you have an XOR gate which is just one level but the gate is complex and when it comes to D2 there is an AND gate and an XOR gate so the delay from the present state to the next state is different for different the flip flops different paths this should be kept in mind sometime when we see a picture like this that is not evident but that you should not lose sight of the detail that inside you should be able to view the D2 D1 D0 as separate paths with different levels and different complexity and so on. So that is why I show this picture so keep that in mind so let us move on let us see the more complex counter suppose I want to design a mode 6 counter with up and down control that means there is a control called up down when it is 1 it will when it is 0 it will down count when it is up it will up count ok. That means we have to have an up down control when it is say 0 it will be down counting that means if it is we start with the reset 0 when the clock comes if the up down is 0 then the next state will be 5 then 4 3 2 1 if it is 1 then from 0 it starts 1 2 3 4. So how do we accommodate this that is a question but we know that in a synchronous counter the present state is upon the clock on the next state so all this has to whatever happens has to happen at the input D here that means when the clock comes this is only moved here so this up down should come in the next state logic ok. So essentially we give an input to the input it is a single bit it is shown as a bus but it is just a single bit so when it is 0 it down count when it is up it is up count so essentially we change the truth table of the next state logic then you get up down counter. So let us look at the truth table so now the truth table is becoming little more complex you have the present state which is Q2 Q1 Q0 and the input up down. Now the next state we decode as a function of the present state and the inputs ok so you have a column for D2 column for D1 typically in manual process you will be called the ones form the min terms minimize it and all that. So but as I said we are going to use the higher level tools which will do the minimization so we do not bother about the whole minimization process we try to represent this table in some form of hardware description language maybe we will enumerate every case in the most simplest case or in some abstract form in a high level form we will represent this truth table very concisely when we go to the VHDL language. But the thing is that we get three equation now it is a function of not only the present state Q2 Q1 Q0 it is also a function of the input. So we say in this case next state is a function of the present state and the input so if you go back to the diagram so the next state is a function of the present state which is fed back from the flip flop and the inputs ok. This shows that you can give you know you can give a very complex counter suppose one issue with this reset is that this reset is asynchronous ok. It means that as soon as you make the reset active this goes to 0 but if you remove the reset and if the clock comes immediately then this will become 1. So otherwise all the other counts starting once you start the other counts is of the duration of one clock period ok. So you can watch this the waveform so the waveform shows that this count remains there for one clock period but the 0 may not remain in the case of asynchronous reset maybe we will reset the counter here immediately the clock comes then the 0 will be there only for a short duration. So there is an issue in this case with the starting state the 0 state then once you start it then everything is ok but the next 0 which is kind of coming back will be ok but the starting 0 is an issue. So if you want that to be perfect of at least one clock duration then you have to have a synchronous reset. So it is very simple you give a reset here and change the truth table and say that when the reset is asserted this is 0. So clearly upon next clock the 0 will come here and that will be remembered for the one clock period. So you could have any kind of suppose you want to load some value into this counter and start counting from there. Say you want to load 3 very simple then you give a load control here and an input then when the load is high you say the next state is that input there after if the load is low it counts depending on up and down then you get a preset of a counter ok. So it is very simple you can write the truth table with the load the reset up down everything any complex counter can be made and if you take if you think of it it is very easy even in terms of the high level function the reset can be thought of as a MUX here when the select line of the MUX is the reset line when that is asserted we give a 0 and it goes there ok things like that so or a MUX here at the output and we can view all these in terms of various multiplexers which we will see probably later for the time being let us assume that the combinational circuit functionality is changed by the truth table so that is what I wanted to convey. So you can have in principle various synchronous control like you can have a control called count by 2 if it is active the counter will count by 2 like instead of 0 1 2 3 it might go 0 2 4 6 0 like that you can have a synchronous reset very properly it will reset and this is very important because many counting applications is used for timing the precise timing and we cannot have any ambiguity that one state is only half. So in such cases it is better to have synchronous reset we can have a control called skip 3 if skip 3 is active then 3 will be skipped and as I said you can preset some values by asserting load then there is an input 3 bit input which is this shows the D in 2 D in 1 D in 0 so that is the meaning of this so when the load is high this value is loaded onto the counter so all this can be incorporated that you should know so you know all about how to build any counter which can count in any sequence any complex operation you need not worry like you need not learn what is inside and worry about it and moreover we are designing complex system so that we can use hardware description language to represent all these behaviour in a little more abstract way than enumerating like in a truth table we will see that when we learn the VHDL. So the next question I want to ask is that you we have talked about a synchronous sequence you know sequential circuit synchronous counter can we have an asynchronous counter that means we do not have in this case what happens is that when the clock comes the next state comes to the present state that means if we start with 0 next clock comes the 1 comes here and that goes there and it decodes 2 and 2 is ready next clock comes 2 comes here. But the all the intelligence is in the combinational circuit but if you see the purpose of the flip-flop is to kind of hold the value here so that this logical work properly and secondly it is precise timing when the clock comes the things change at the exact instant okay of course with the delay if the delay is kind of fixed then at the same time at the same interval this change happens over and over. But the question is that that is if that is the purpose why not suppose the propagation delay of this flip-flop is 1 nanosecond say then what we will do is that between D2 and Q2 between D1 and Q1 D0 and Q0 we insert buffers of 1 nanosecond delay and make at the beginning make this present state 0 by asserting a signal then will it count 0 1 2 3 like that that is the question. We have no control over the timing it will go very fast as fast as the depending on the delay but will it work so the answer is that it will work there is no issue but you should remember there is an issue here which I have mentioned earlier the decoding circuit of D2 D1 D0 might incur different delays with respect to this point okay we might put 1 nanosecond buffers exactly here but when from the present state to the next state there are 3 circuit 1 for D2 1 for D1 1 for D0 maybe 1 is slower than the other that can create problem. So take this case we have a count 1 here 0 0 1 which is going to count 2 which is 0 1 0 now what happens is that there is a change in Q0 Q1 and Q2 does not change assume that the Q1 is faster than Q0. So what happens is that before Q0 transit from 1 to 0 Q1 transit from 0 to 1 so in between going from 0 1 to 2 there is a for a brief duration there is a state called 3 or the count called 3 now if that remains there for this propagation delay then the old game can change the next state becomes 3 and we lose control. So the trouble with asynchronous circuit is that it is very fast when you want very high speed operation this is good but wherever there is a feedback it creates problem because there is unbalanced path delay in the multiple path and there could be raises and we call this raise 2 output can raise and there could be intermediate values things can go wrong. So that is why we use as far as possible synchronous circuit particularly when there is a feedback it is easy to design synchronous circuit than asynchronous circuit. But whenever there is no kind of feedback one can go for asynchronous circuit so that is summarized here yes synchronous circuit is possible but the trouble is with unbalanced path delay there could be raises in output it is difficult to design and control it is very fast ok. So that is about the asynchronous counter or asynchronous sequential circuit. So let us move on to the timing part of the synchronous counter we have designed. So the question I want to ask you is that what is the maximum frequency of this counter that means we have a clock how much frequency the maximum we can apply to this clock ok that depends that has to be determined because above which it may not work ok. So definitely that depends on the delays of the blocks involved the delay of the flip-flop and delay of the next aid logic and you for a moment you think a clock edge active clock edge comes here then the present state will change after TCO delay then that comes here it propagates through the next aid logic and comes here ok. So there is a TCO delay and TCOM delay and there are 3 paths you know D2, D1, D0 not only 3 paths I mean 3 outputs but there could be 9 paths we will see that 9 paths but because for each D2 the input can come from Q2 or Q1 or Q0 there are 9 paths and we have to take the maximum delay. And now you know that before the next clock edge comes data has to be steady here sometime before call setup time. So we have seen that for the flip-flop to work properly the data should appear here sometime before the clock edge and it should remain sometime after the clock edge. So the clock period should accommodate all that delays and we will see it pictorially. So let us take this as a clock and a clock edge comes here. So say it takes this much time the TCO time for the data to change here. So it changes there you see the present state changes there and then it propagates through this combinational logic and the data at this point the data changes here after a combinational delay. So that is what I have shown after the first clock edge the data changes at this point after the TCO delay and at this point after the TCOM delay. So the data arrives here the TCO plus TCOM delay after the clock edge but we know that before the next clock edge comes the data has to be here sometime before call setup time. So now that means there has to be some gap at least this line and this line can touch but it cannot go before. So that means the total the clock period T clock should accommodate TCO, TCOM and T setup. So that is what is shown here the minimum clock period minimum you can go should be greater than TCO maximum clock to output time, TCOM maximum like what there are many paths we have to pick the maximum delay and the maximum setup time and that gives the minimum you can go. The maximum of frequency will be less than 1 by T clock mean because this is becoming this is the maximum value so the frequency maximum we are taking it in the denominator. So f max should be less than 1 by T clock mean but it is not good to like in this like it is not good to keep it equal then any temperature variation if the propagation delay becomes more then there is an issue. So we normally give a margin and that margin is called slack which is the all these three quantities subtracted from the T clock will give you a slack okay. But the surprising thing is that in this equation the whole time does not picture at all okay does not looks like it does not matter the whole time does not matter for the maximum frequency maybe at the beginning it is little bit of a surprise but then we have to see whether the whole time is kind of met in this case and what is the condition that it can be violated. So let us look at this picture the whole time say when a clock edge comes okay here you say let us take this clock edge clock edge when the clock edge comes it say that whatever data was there before the clock edge that should remain for some time afterwards okay. But we know that when a clock edge comes the data at this point is going to change only after TCO plus TCOM delay okay. So the whole time if TCO plus TCOM you know that the next state will change only after this propagation the clock edge comes it propagates here then it propagates here then it changes there. So it is enough if the whole time is less than TCO plus TCOM or other way TCO plus TCOM should be greater than that whole time and mind you now we have to take the minimum TCO. In the maximum frequency case we pick the maximum delay of the TCO and TCOM to accommodate the T clock but in this case the minimum is the constraint because there could be a case where one of the say Q0 is very fast TC Q0 is fast and from Q0 to one of the input is very fast then there could be a problem. So we say TC or MIN plus TCOM MIN should be greater than the T whole max okay. Now that looks at least pictorially it looks kind of an impossible condition to violate and now if you pick a flip-flop okay and just analyse the timing of the flip-flop and if the flip-flop itself the TCO is greater than the T whole of the flip-flop this cannot be violated at all the TCO MIN or the least TCO is always greater than the whole there is no question of this violation okay. So it looks like whole time can be violated but in whatever in this our analysis there is something hidden which we have not stated so that is very important. So here we have assumed that the clocks for there are three clocks going to three flip-flops but we assume that the clocks are arriving at each flip-flop at the same time so but in real life that may not happen and that is called skew the clock may be skewed with respect to each other that means the clock 2 may be coming earlier than the clock 1 and clock 0 may be arriving later than the clock 1 and so on okay. So this equations will change and there could be whole time violation when there is clock skew and the worst case can happen when there is no combinational delay like assume that for some reason the combinational delay is small or nil and you already know that we build a shift register the one flip-flop output will go to the next flip-flop input. So in such case there is no combinational delay and if there is a clock skew there can be whole time violation okay. So this is important to remember and we will analyse the case with the clock skew but this is the main as far as the sequential circuit is concerned. The next important thing is the maximum frequency of operation and the whole time violation. These two things are the important timing parameter of the sequential circuit synchronous sequential circuit and mind you that is built on the symbol combinational delay and the flip-flop timing parameters like TCO, T setup and T hold. So with very simple things the propagation delay of the combinational circuit and the propagation delay of the flip-flop the setup and hold time the next level of the timing details are built on this the maximum frequency and the hold time violation. So that is at the next level that is the most important thing. So quickly I have stated whatever I have told these are the basic parameter and rest of all is built on that and we assume that the clock is not skewed in this case when there is a clock skew we have to analyse it and we will analyse it later and the hold time violation okay. One thing to remember suppose we build a circuit like that and we gave some clock we suppose we gave say 500 megahertz clock here which gives say 20 nanosecond 1 megahertz 2 nanosecond clock period and if this is violated then what to solve the problem you have to kind of increase the clock period. If there is a this inequality is violated to solve it is to increase the clock period but assume that this is violated TCO min plus TCOM min is greater than the hold time the increase in the frequency won't help at all because there is no T clock period in this inequality. So there is no point in suppose this is violated the only way is to increase the combinational delay. So we may have to when there is a hold time violation we may have to introduce additional delay in the combinational path that is how to sort out the hold time violation that is what I stated here when a minimum clock period condition is violated this can be met by increasing the clock period. But when there is a hold time violation you need to increase the combinational delay then I stated in a flip flop TCO can be greater than the hold time and if no clock skew the hold time cannot be violated. But when there is a clock skew and when the combinational delay is minimum or 0 like in a shift register this hold time violation can happen then you have to introduce the additional clock delay. So let us look at the number of paths probable paths in the previous circuit. So suppose in the case of a mod 6 counter there are 3 flip flops and total number of probable register to register paths are 9 because for from each qi to each dj there could be a path okay. In the case of a very simple sequence it may not be there but in general there could be a path from like we know that the q0 is a function of sorry d0 is a function of q2 q1 q0. So when you build a circuit for that d0 there is a path from q0 there is a path from q1 q2. So 3 paths for each d0 d1 and d2 there are 9 paths. So essentially as far as the timing is concerned it is to analyse this register to register path okay. It need not be synchronous counter like in timing analysis we look at from each register to one source register to the one destination register path need to be analysed for to find the maximum clock frequency and to find the hold time violation. So that is the basic game. So in general when you look at the sequential circuit there is some source register which is holding some value which is passing through a combinational circuit for some computation and it reaches the destination register and we have to make sure that this like inequalities are met. So here that there is a source register which supply the data to a destination register through a combinational circuit then the clock min should be greater than tco plus tcom plus or equal to tco plus tcom plus t set up with some margin and the hold time violation to avoid then you have the tco min plus tcom min should be greater than the hold minimum. So this is the most general case of the timing a register to register path wherein you can find the maximum clock frequency and the condition for hold time violation. So we have abstracted it from the taking a synchronous counter and example and come to a very general sequential circuit need not be synchronous counter anything can be analysed in this manner. So let us move on so let us make things little more complicated or complex let us take a flip flop we know that the set up time and hold time is specified at the input that means the we know the timing parameters state that with respect to this clock there is a set up time the data has to be set up sometime before data has to be held sometime after. So we take an example of set up time being 2 nanosecond and hold time being 1 nanosecond then the data width the minimum width of the data is like that data is changing from 0 to 1 just before the 2 nanosecond it remain for 2 nanosecond up to the clock and 1 more nanosecond and it changes okay. But many a times like we may take this input at a pin on a chip like you know on an FPGA and we would like to know and that might like the a wire is going from the pin through some buffers and reaches here. So there could be additional delays in the data path as well as in the clock path but for analysis we will separate this case it is easy to analyse and grasp the concept and then we can you know you can put it together.  We would like to know what is the set up time and hold time with respect to this point because we have control over this point. We are supplying the data from outside at this point and we are not worried about the set up and hold time here that does not help us because there is an additional 2 nanosecond delay. So whatever we put here up here here after 2 nanosecond so you see this data here comes earlier by 2 nanosecond d dash so I have moved the data at this point by 2 nanosecond to the left. Now assume the clock is same so what is the new set up time at this point d dash. Now the set up time you see with respect to this clock set up time has increased because the data at this point has to be set up 4 nanosecond before because this 2 nanosecond plus this 2 nanosecond delay data d dash has to be set up 4 nanosecond before the actual clock. So this 2 nanosecond is added to the set up time set up time is increased. Now hold time you see hold time is 1 nanosecond towards the left ok now one thing to remember is that set up time is defined as the time before the clock edge the data has to be set up. So and the hold time is defined as the data has to be held after the clock edge but in this case you know the data is removed before the clock edge so it becomes negative. So whatever was 2 nanosecond this delay is you know you have 1-2 you get minus 1 nanosecond and do not worry about then minus 1 nanosecond it essentially means that you can remove the data. After the clock edge when the hold becomes negative in the opposite direction it means that you can remove the data at this point even before the clock edge ok. So if you do that at this point correctly the data will match this window of the set up and hold time. So it essentially means whenever you have a delay in the data path or the this path then the set up time increase and the hold time decreases and the hold time can become negative you need not worry it means that the data can be removed even before the actual clock edge. So that at the input of the flip flop everything happens very correctly so that is the case with when there is a skew in the data path let us analyse the other case that when there is a skew in the clock path what happens ok. So this is summarised whatever I have told a delay in the data path will increase the set up time decrease hold time minus t means data can be removed before the active clock edge set up time is defined before the set up before the clock edge and the hold time is defined after the clock edge. So whenever it goes in the opposite direction it is a negative value so that is what it means so let us take the next case where there is a skew in the clock path and that means we have a pin here we give the clock and that suffers a delay of 3 nanosecond before reaching the this particular flip flop and we would like to know what is the relation of the data set up time and hold time with respect to this clock but that is where we have controlled. So the actual clock here is shown here this is the clock and it has a set up time with respect to this point 2 nanosecond and hold time 1 nanosecond so in the normal case the data appear here with you know because there is a 2 nanosecond here. And the clock you see here the clock dash will appear earlier to this clock by 3 nanosecond so that it will appear correctly here. So now you can see that this edge of the clock is moved left by 3 nanosecond ok. So now at this point our timing is with respect to the new clock or the clock dash. Now you see the data has to be set up at this point after the active clock edge so the set up time was 2 nanosecond but now it has become 2-3 nanosecond which is –1 nanosecond that means data is set up at this point after the clock edge with respect to this clock point. So that is the minus but it has to be held for 1 plus 3 nanosecond 4 nanosecond. So the hold time is increased by 3 nanosecond by this Q. So it means that if there is a Q in the clock path the set up time is reduced by that much and the hold time is increased and in this case set up time can become negative it means at that point with respect to this new clock the data is set up after the clock appears here. So that at this point everything you know works correctly. So that is what is summarized here when there is a delay the set up time with the new reference point is decreased and hold time is increased and negative set up time would mean that it can be set up after the reference clock ok that is what about. So this is what I have you know covered in the last few slides basically we have looked at the structure of the synchronous sequential circuit. We have taken an example of a synchronous counter we have looked at the main components like the flip flops the next state logic you know which decodes the present state make the next state. So basically two components next state logic which decodes the present state and the inputs when you give inputs you give inputs to the next state logic that it can control the next state in a desired way like a synchronous reset load and up down and things like that any complex operation only thing is that we change the truth table accordingly then you get the functionality and we also said that you know there are you should not lose sight of the detailed view because there are lot of paths within that simple diagram which should not be lost sight. And we have looked at the asynchronous circuit and we have seen there could be races because there is unbalanced path delay in the case of feedback. So it is difficult to design and control so we stick to the synchronous sequential circuit synchronous counter in that case we have looked at the timing and we have looked at the condition for the maximum frequency of operation. We have looked at the condition for the whole time violation these are the two main things which is built on the basic timing parameters. Then we have looked at the case where there is a what happens to the setup time and whole time when there is a skew in the setup path when there is a skew in the clock path what happens with the setup and whole time with the new reference point that is very useful in analysis if you do not grasp that many a times you can analyse things properly. So let us move forward let us look at how to go about designing some system digital circuit. So let us move on say take an example suppose I want to design a 60 second simple timer okay which counts like say 0 to 60 that is all and display it maybe for some practical purposes like we have a counter which counts little accurately from 0 to 60 in sequence 0 to 59 mode 60 counter very precisely like every 1 second it should change. So how to go about designing that is a very simple thing let us start with a very simple design. So how do we design such a thing okay so let us look at the to the slide so the first thing you need is a 1 second clock but you do not get a 1 second oscillator you have to build oscillators are high frequency oscillator you cannot have a crystal vibrating at 1 second period. So you have to have high frequency oscillators maybe 1 megahertz maybe 10 megahertz or 500 megahertz then you divide using counters to get a 1 second pulse the moment you have a 1 second clock you can give it to a counter and start counting. So let us put that in the picture so we have a clock oscillator which is of high frequency maybe let us assume it is a 1 megahertz clock and then we put a divider so if you put a 1 megahertz clock you know that it has to be divided by somewhere around you know nearing around 2 raised to 20, 2 raised to 20 is a binary number more than 1 meg but you need at least 20 flip flops with some mode to like mode 1 meg counter to divide this and here you get a 1 second pulse ok. So we will make a very very very simple design so for to count from 0 to 59 we will put a counter 2 part 1 least significant digit will count from 0 to 9 when it reaches 9 it will increment a mode 6 counter which is counting from 0 to 1 like that. So we will put a BCD counter which counts the least significant digit when it reaches 9 it will increment a mode 6 counter which goes from 0 then when it reaches 9 it goes to 1 and so on. Now we have to display it so we need a 7 segment some kind of display simple thing let us take a 7 segment LED so we need a BCD to 7 segment decoder here we can use still use a BCD to 7 segment decoder or a mode 6 to 7 segment decoder then we can drive some LED to light it up ok it is very simple when you have given some simple design like this you are able to design from 1 and you know you start with the clock you put the divider, put a counter, put some decoder things like that when you are thorough with the digital design simple design like this can happen in a very very from 1 and 2 other and you take a paper and do it and if you try to design this in a using a hardware description language it is very few statement maybe one statement few statement for this divider few statement for this and something for this and you can connect it the output to the LEDs and it works perfectly fine you can add different control like reset and what not. So all that we have learned you know you can incorporate many other controls in the counter if you need ok but I talked about at the beginning of the lecture there is function there is timing there is electrical spec so let us investigate whether that does that matter here what is the function ok function we have designed ok. So is there any timing related issues here ok or even function like area such issues can be addressed in a simple case like this ok. So like if you look at this counters it count very low frequency like it counts kind of 1 second so it is not a very high frequency design but you take this divider you see the clock of the divider is 1 megahertz so at least 1 megahertz so this divider is working at a high frequency than this counter. The flip flops here are clocked at 1 megahertz at least some flip flops are clocked at 1 megahertz depending on the design. So it dissipates lot of power here ok. So that is an issue to keep in mind you know there is a high little high frequency part compared with this secondly I said this need to be accurate how do we make sure that this 1 second counter is accurate and how to to improve the accuracy. So that you should know that suppose this clock source has some drift say it goes say it is a 1 megahertz you know clock source suppose it drifts little bit you know say some parts per million it drifts then you know that the drift is divided by this divider. So since it is drifting in the higher frequency the drift in the lower frequency is so much divider. So the accuracy improves so it shows that if you instead of a 1 megahertz clock if you go to a 10 megahertz clock with the same drift you will get a better accuracy in terms of the accuracy of 1 second. So it probably is worthwhile to go for a higher clock frequency then you should know that the divider size will increase like if you go to 100 megahertz the number of flip flops will increase and the frequency of operation will increase and the power dissipation will increase. And suppose if it is a battery operated thing the higher accuracy might mean lower battery life and that you should know ok. And similarly look at the area of this say the BCD counter you know that it counts from 0 to 9 needs 4 flip flops and mod 6 counter need 3 flip flops and that means it is 7 flip flops. So can we reduce this number of flip flops ok. So think for a while this design takes 7 flip flops can we reduce for the number of flip flops for the same functionality. So the answer is yes because here we have split the counter like a mod 9 counter or a BCD counter and a mod 6 counter there are 4 bit output here, 3 bit output here. So for a while let us assume what we need is a counter which count from 0 to 59. So assume that means we are not splitting it we are putting it together ok that it counts it is a we can put a 6 flip flops which can count up to say 64 and but we will design set that it count up to 59. Then we instead of having a BCD and mod 6 counter we design a counter which is mod 60 counter that means we put 6 flip flops and redesign then we say 1 flip flop. But the complexity is that now here we had a BCD to 7 segment decoder decoding 4 to 7 like 4 to 7 decoder here it is 3 to 7 decoder but in that case we need a mod 62 to 7 segment LED decoder ok that means we will have some 6 lines here which is using a combinational circuit you have to decode as 2 7 lines maybe we will we do not know the complexity of that decoder depends on the input output pattern we cannot say anything about the redundancy. So if you go for a mod 60 counter we may say 1 flip flop here but maybe the decoder here can become more complex than this separate decoder I do not know unless you literally try and find out you should not assume that that will be simpler than this case need not be. So one has to verify that whether that will be a simpler thing and definitely you know that here it is driving the LED suppose the LED to be very bright will take some current. So maybe this BCD to 7 segment output pins has to give some 20 to 100 milliampere for it to be visible at a distance so there is an electrical spec which needs higher current drive here. So even in a simple circuit like this there are issues of the high frequency power dissipation the area conflicting requirements of area we do not know we cannot a priori say that this is a better scheme than mod 60 counter or anything like that. So my advice is that seeing something simple you should not assume that is very simple there are no issues there may be issues like the accuracy as we see area then the timing then electrical specifications and things like that. So this we should keep in mind whatever be the design is small or big there could be these issues to be thought about and the textbook may not teach you all this it is for you to apply whatever you have learned in the basic and apply to the particular case and that comes with the experience comes with many a times working on simple projects, implementing things then only you will be sensitize then only you will be quickly able to catch on this issue and solve the issue that comes with the experience comes with thinking in learning it is not that you learn everything you understand everything but thinking is an important thing and what you have learned in the textbook you have to apply to the real life then only you can find the issues in real life and that is the true engineer is the one who finds the issues and quickly identify the problem areas and try to solve it and there is no one can say the systematic approach will help but many a times that alone will not help in a complex system some issue come up many a times you have to quickly use a very off repeated phrase you have to zoom in to the issue and sort it out and that comes sometime very quickly without like you cannot go from remembering all the issues and one by one looking at it many a times it clicks in the mind that comes with the experience that comes with your own deep understanding of the issues and the mind works very quickly seeing the behavior you will be able to quickly debug you know that is one issue I want to emphasize with the real life circuit the debugging is very important that when you have a problem you should be able to quickly sort it out and debugging is not limited to the hardware it can be the software it can be a mechanical system it can be true with the mathematics you know you do not call debugging a theorem or debugging a proof but essentially that is what is done you are like you are trying to suppose you have a hypothesis you are trying to prove it and you try work out something something goes wrong so that what things go wrong should point you out what is the what is wrong with the hypothesis or what is wrong with your approach to proving it and things like that. So I would say that is debugging you know that is debugging the mathematics so you can debug a mechanical system something is going wrong something is not moving properly you have to debug it the concept the ideas the technique the thinking is same irrespective of whether it is abstract whether it is real life sometime you will be surprised to see very lowly technician applying their mind you can learn a lot when you see the real technician solve some problem in their domain they experience people go in the correct sequence of assembling something dismantling something trying to locate the issue with the problem and sort it out this is an eye opener maybe they are experienced they are doing the things day in day out but the engineering domain needs such approach such thinking such deep understanding experience and learning with the practical example always try to implement and try to if something goes wrong try to find out what is going wrong so that you go wrong less time many times people repeat that you have to learn from mistake yes you have to learn from mistake but in your career in your life you should make less mistake like you should learn as much as from the mistake that means once you make a something goes wrong then you should analyse it and learn it thoroughly so that that is not repeated so the next slide I will give a I will just sensitize we are going to a bigger design ok really we will take a complex design and see how to you know how in a complex case the design can be done so I did not start the lecture and just now because I will have to terminate it half way so the next step we have taken a very simple case and see how the digital design is done the next step is that we will take a reasonably complex design and see how the design methodology can be applied in terms of the function timing the issues involved how to go about knowing with the minimum knowledge how we can design is what I am going to cover in the next lecture so I have covered some minimal things but these are very important things I have covered so please go back review try to grasp in your mind you know think about it work on a paper try to understand ask questions to yourself like you should have the doubt write it down now this is a video lecture I have no way to interact with you but then you write down your question logically then try to answer it look for the answer probably you can contact me if you are stuck very much you can contact me in email I will try to answer so I wish you all the best and in the next lecture we will move with a with a complex case and thank you.


In the previous video, I showed how turning the crank on this machine generates 20 different frequencies, also known as harmonics, which are turned into cosines here, multiplied by coefficients, then summed, magnified, and the resulting function plotted here on the front. This process is called synthesis. But this machine is called a harmonic analyzer, which means it can be used to solve the much more difficult inverse problem called analysis. For example, if I want to plot a particular function here, how do I set the amplitude bars to produce it? To illustrate how this machine does analysis, let's start with a square wave. First, we use some unique properties of the square wave. Since it's periodic and even, all of the information that function carries is contained in half a period. So we'll take that half a period and sample it at 20 equally spaced points. We use the values of these points as the inputs for the machine. When we turn the crank, we produce a new function that reveals the correct coefficients. To see how we get these coefficients, we'll look at the side of the machine. As I turn the crank, the tips of the rocker arms form a sinusoid. The indices on the rocker arms run from high on the left to low on the right. I'll flip the video to make it a little more intuitive. When the rocker arm tips are lined up in a straight line, we'll call that crank number zero. If the horizontal axis runs from zero to pi, and the vertical axis from minus one to plus one, then we can describe the position of the rocker arms with a cosine. Every two turns of the crank increases the frequency of the cosine by one. At these even numbered cranks, the values of the function on the platen yield the coefficients we're looking for. Let's rewind and watch the plot and the rocker arms simultaneously. If we pause briefly at every second crank, a point is marked on the function. We create a total of 20 points. If we look at the output from the machine and compare it to a sink calculated by a computer, we see that they are very similar. Now, we'll take the data points from the sink, scale them, and use these values on the rocker arms. Remember that our goal is to program the analyzer so that it will plot a square wave. Now, as I turn the crank, the pin writes a horizontal line, then drops and writes another flat section, which amazes me because we're adding only cosines, and then it rises to write another horizontal line. Of course, what we're seeing is a square wave. What I've just shown with the machine is an essential feature of Fourier methods. I can take a function, perform harmonic analysis, extract the coefficients, and then synthesize that function to approximate the original. So, now that we see that this machine can do harmonic synthesis and analysis, I'll show you in the next video some details about how to set up the analyzer to perform these calculations. I'm Bill Hammack, the engineer guy. Next up in the series is operation. If you haven't seen them already, there's also the intro and synthesis videos. You can learn more about the book here, and if you really want to learn more about the book, watch the page by page. If you're a fan of oscillatory motion, you got to watch the bonus rocker arms video.


When you are young, you are as free as the wind. You can try out different careers, start businesses, fill and start all over again. It is time you build yourself a future endeavors by studying, working and exercising. There are, however, some key things you should avoid at this stage. In this video, I'll be sharing with you the seven liabilities to avoid in your 20s. 1. Not having a life insurance. A healthy-looking young man walked into a store to buy some groceries and then slumped at the counter while trying to pay. He was rushed to the hospital. When he becomes conscious, he was told he has brain cancer and asked whether he had insurance and he said, No, what do you think will happen? If you think you are too young to have any ailments, read the history of Stephen Hawking. A renowned American scientist who is diagnosed with ALS, a model in your own disease at the age of 21. You may not look at it at the moment, but anyone can get sick. The only way to plan for this sufficiently is to have comprehensive health insurance. Having health insurance gives you peace of mind over cost of treatment when something happens to you. It gives you the liberty to spend your income and investment and savings while the insurance company covers the full cost of your recovery. It also gives you access to more job opportunities because employers are more likely to hire people with health insurance than those that do not. Not having health insurance is a big liability at this stage. 2. Attending an expensive college without a plan. Going to Harvard or Cambridge for a further degree is a huge boost for your career. Most multinationals hire excellent candidates from the schools. The schools only take the best of the best. So, getting in is even a challenge in its own. The school, however, have very high tuition fees as well. Most people take student loans to pay for tuition. While this is a great strategy, if you are not prepared for what comes next, the debt from students' loan can become a liability. Only take a loan if you can repay without going bankrupt. And even when taking the loan, ensure you have put in place plans to pay back. Many people go to these colleges hoping to get a job that can take care of the debt, but hope is not a strategy. You need to know what the job prospects in your area of study are. You have to plan to intern during the summer and get to know some professors in your schools who can recommend you for internal scholarships that you can use to upset your student loan. Taking a loan for college is a smart move, but only when it is backed with a carefully formulated strategy that ensures the loan would be repaid promptly when due. Having a student loan to repay and no job is a recipe for unhappiness. 3. Spending more than you earn There are so many things to buy. The number of things one can own is endless. The resources to purchase them are however limited. There are also very few things that we need. How many shoes do you own that you have not worn in years? How many shirts and trousers do you own? How many of them do you actually wear? Why buy things you don't need? When you are young, you are usually at the stage of building your wealth. Spending more than you earn can only put you in debt and debts can keep you poor. Therefore, you should create a budget for a month and stick to it. Do not purchase anything outside of your needs or time. You will get used to it. If you still find yourself making impulsive purchases even after creating your budget, then anytime you want to make a purchase, ask yourself this question. Can I do without it? If your answer is in the affirmative, walk away. 4. Not having a savings This is a liability to be avoided at all costs. At every point in time, as a young man, you have to have your living expenses for 3 to 6 months saved up. This is because of the nature of jobs you will likely hold at this stage. There will hardly be a permanent job and you can be fired at any time. The economy is unpredictable too. The company can decide to downsize and when this happens, you want to be prepared to deal with it while still pursuing your dreams. Having a savings gives you backup cash to pay for personal development courses, books and even networking conferences in your area of interest. Savings can help you quickly replace your film if it's stolen and pay for your rent if your salary is late. The advantages are numerous. 5. Not having a financial plan To spend is easy, but to make money is not as easy. It only seems fair to maximize our use of money since spending it is way easier than making it. Having financial goals is the first step to financial planning. How much do you want to be worth in the next 5 years? Clearly defining your goals can help you make better financial plans. According to Confucius, a Chinese philosopher, a man who does not plan long ahead will find trouble. Working without a financial plan can be a liability. You will likely spend without purpose. Financial plans help you make every dollar count. That way, you maximize your income towards your sustenance and growth. 6. Getting an expensive apartment Leaving in an expensive apartment can be a liability at this stage, especially when you can barely afford it. It puts unnecessary pressure on you. The apartment comes with both expensive rents, utility and transport. It even gets better because of the neighborhood. You might feel the need to blend in. This might mean wearing more expensive clothes than you can ordinarily afford and calling Uber when you can use the bus. Getting an apartment that is barely affordable can be a liability at this stage. 7. Having too many subscriptions There are enough applications today to keep a person occupied all day. Some of them require subscription fees to maintain. A popular example is Netflix. People usually subscribe with the hope that they will have the time to use up the subscription. But sometimes, they get caught up in work, but they end up not using them at all. They also just can't seem to find time to unsubscribe from all the magazines, websites and applications they have subscribed to. So, there are emails are full of clutter and they continuously receive debt alerts from subscriptions they cannot even remember. Having too many subscriptions than you need can be a liability in your 20s. It can both deplete your income and take up space in your email, making it hard to sort out relevant information. You may have some or all these liabilities combined, but the good news is that it is not the end of the world. You can start now to write down your goals, then work on yourself with everything you have got. Thank you very much for watching our videos. 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