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And I said, how many B's? You went through the string again. You went through the string 26 times or 27 times. That's a lot of times through the string, right? Here's another example. Everyone have their textbook? OK. How many A's in Pat and Patel? Everyone got that number, right? How many B's? 42. Exactly. All right. Oh, yeah. So the real question, if I had asked you to do that, let's say you were getting paid. | [
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Oh, yeah. So the real question, if I had asked you to do that, let's say you were getting paid. You're getting paid to count the number of A's and B's and C's in Pat and Patel. How would you do it? Would you do it the way you did it with a little string? Would you say, let me look for A's? OK, I'm done. Let me look for B's. Or would you do it a different way? Yeah, go ahead. Can you repeat the question? Yeah, so you can go through the whole book. | [
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Or would you do it a different way? Yeah, go ahead. Can you repeat the question? Yeah, so you can go through the whole book. And then maybe I don't need to use sophisticated data structures. Maybe I can have a piece of paper with letters A through Z on them. And every time I see the letter A, I'll make a mark on A. When I see the letter C, I'll make a mark on C. But then I just go through the book one time, which is a lot faster than going through Pat and Patel 27 times, I think. | [
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When I see the letter C, I'll make a mark on C. But then I just go through the book one time, which is a lot faster than going through Pat and Patel 27 times, I think. Although you should enjoy reading Pat and Patel, but maybe not 27 times. So here's another algorithm. So for a longer string, maybe what we do is we set all our histogram to zeros. And then for every character in our string, we'll go through it once. | [
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So for a longer string, maybe what we do is we set all our histogram to zeros. And then for every character in our string, we'll go through it once. And then we'll just increment the appropriate histogram bin. So if we see the capital letter T, we'll go to the T and increment it. If we see the number 5, we'll say, well, that's not a letter. We'll go to the non-alpha bin and increment it. | [
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If we see the number 5, we'll say, well, that's not a letter. We'll go to the non-alpha bin and increment it. So figuring out, well, which bin, that might be a little complicated. So we're going to have to figure that out. There's one more I want to show you. We have a few more minutes. OK, good. So what if instead we did this? What if instead we said, well, let's make the inner part simpler. | [
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] |
OK, good. So what if instead we did this? What if instead we said, well, let's make the inner part simpler | [
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If we see the number 5, we'll say, well, that's not a letter. We'll go to the non-alpha bin and increment it. So figuring out, well, which bin, that might be a little complicated. So we're going to have to figure that out. There's one more I want to show you. We have a few more minutes. OK, good. So what if instead we did this? What if instead we said, well, let's make the inner part simpler. | [
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OK, good. So what if instead we did this? What if instead we said, well, let's make the inner part simpler. I don't want to do a lot of calculation. I want to just make it easy. So let's build a bigger histogram. Let's have, let's see, ASCII has 128 characters, right? So I have 128 characters. And then what I'll do is I'll go through the string one time. And every time I read an ASCII character, I'll just say, oh, that's ASCII character number 35 hex. | [
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And then what I'll do is I'll go through the string one time. And every time I read an ASCII character, I'll just say, oh, that's ASCII character number 35 hex. Let me go to entry 35 hex, add 1 to it. And so do no computation at all to figure out what it is. I'll just go add them up, whatever the index is, whatever the character is. I'll use that as an index into my array of 128 things. | [
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I'll just go add them up, whatever the index is, whatever the character is. I'll use that as an index into my array of 128 things. Add 1 to it. And then when I'm done, well, there's lowercase a and uppercase a. So I'll add those two numbers together. And that'll give me my a. And lowercase a, uppercase a, I'm sorry, lowcase b, uppercase b, add those two numbers together. Done. And then I'll add up the rest of the things that aren't letters. | [
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Done. And then I'll add up the rest of the things that aren't letters. And that'll give me my non-alpha. So now finding the bin is easy, right? It's just, well, whatever the character is, there's 128 of them. Go to the right one. Add 1 to that memory location. But then I have to add some extra initialization. Instead of 27 bins, I have to do 128. I have to do a little extra work down here. | [
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Instead of 27 bins, I have to do 128. I have to do a little extra work down here. So there's some trade-offs. It's a little more work at the beginning and the end, a little easier in the middle. But what's better? So maybe I'll leave you with this. We'll talk about it a little bit. And I'll leave you to think about it. So what is the metric? When you get into later classes, or maybe some of you have seen this, you might talk about things like computational complexity, which usually map to something like, well, how many instructions does it take? Or how much time does it take? How many cycles, clock cycles? How long does it take to run your program? That's going to have a lot of factors that change the answer. | [
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And I'll leave you to think about it. So what is the metric? When you get into later classes, or maybe some of you have seen this, you might talk about things like computational complexity, which usually map to something like, well, how many instructions does it take? Or how much time does it take? How many cycles, clock cycles? How long does it take to run your program? That's going to have a lot of factors that change the answer. But basically, if you're looking at how many things you're doing in your program, then that's a measure of complexity. | [
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So what is the metric? When you get into later classes, or maybe some of you have seen this, you might talk about things like computational complexity, which usually map to something like, well, how many instructions does it take? Or how much time does it take? How many cycles, clock cycles? How long does it take to run your program? That's going to have a lot of factors that change the answer. But basically, if you're looking at how many things you're doing in your program, then that's a measure of complexity. And you can measure it explicitly with number of instructions. | [
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] |
But basically, if you're looking at how many things you're doing in your program, then that's a measure of complexity. And you can measure it explicitly with number of instructions. You can measure it explicitly with number of clock cycles, wall clock time. Another way you can measure things is, well, how much memory do I need? Do I need only a few bytes? Do I need a kilobyte? Do I need a megabyte or a gigabyte? Or do I need a terabyte? Do I need to have blue waters to run this thing? Hopefully not, because there's only one of those. | [
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You can measure it explicitly with number of clock cycles, wall clock time. Another way you can measure things is, well, how much memory do I need? Do I need only a few bytes? Do I need a kilobyte? Do I need a megabyte or a gigabyte? Or do I need a terabyte? Do I need to have blue waters to run this thing? Hopefully not, because there's only one of those. So if you need that much memory, maybe it's not your best approach. | [
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] |
Another way you can measure things is, well, how much memory do I need? Do I need only a few bytes? Do I need a kilobyte? Do I need a megabyte or a gigabyte? Or do I need a terabyte? Do I need to have blue waters to run this thing? Hopefully not, because there's only one of those. So if you need that much memory, maybe it's not your best approach. But those are all trade-offs | [
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Another way you can measure things is, well, how much memory do I need? Do I need only a few bytes? Do I need a kilobyte? Do I need a megabyte or a gigabyte? Or do I need a terabyte? Do I need to have blue waters to run this thing? Hopefully not, because there's only one of those. So if you need that much memory, maybe it's not your best approach. But those are all trade-offs. These are different ways you can measure things. | [
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But those are all trade-offs. These are different ways you can measure things. So what about for our problem? Does it make a difference, do you think, for long or short strings? Certainly, probably you would approach it differently for a long string and a short string. Again, try to think about it seriously. If you wanted to do Pat and Patel, you really don't want to do that first algorithm. | [
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Again, try to think about it seriously. If you wanted to do Pat and Patel, you really don't want to do that first algorithm. But if you're going to do a short string, is it really worth getting a table and saying, oh, this string starts with a T? For the short string, it's probably easy enough to just look at it a whole bunch of times and look for specific letters. So maybe the answer depends on the length of the string. | [
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But if you're going to do a short string, is it really worth getting a table and saying, oh, this string starts with a T? For the short string, it's probably easy enough to just look at it a whole bunch of times and look for specific letters. So maybe the answer depends on the length of the string. What if your string is sorted? What if all the letters are in order? That's kind of crazy, right? But to make it easier, then you just count As. | [
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So maybe the answer depends on the length of the string. What if your string is sorted? What if all the letters are in order? That's kind of crazy, right? But to make it easier, then you just count As. And when you get to the end of the As, well, then you go to the Bs, and you count all the Bs. Then you count all the Cs. You're still going through the string once, a lot easier. But why would it, you know, the string wasn't sorted, right? Except you can sort it. | [
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You're still going through the string once, a lot easier. But why would it, you know, the string wasn't sorted, right? Except you can sort it. And you can sort things. And you can do that in linear time for this particular type of problem. So in fact, meaning time proportional to the length of the string is what I mean by linear time. So I could sort it first and then use a different algorithm. | [
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So in fact, meaning time proportional to the length of the string is what I mean by linear time. So I could sort it first and then use a different algorithm. So there's always lots of different ways you can solve these problems. So let me leave you with that thought and think about what's good in these things until Friday. Thanks. | [
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section. Okay, so if anyone wants to chat with me, feel free to stop by. Policy update as of the trouble with the lab, not this week, but last week, your lowest two labs will now be dropped instead of just your lowest lab since AWS, I guess, killed our software right before the deadline. And then I just wanted to do a quick review because a couple of people that asked me about finding all the notes and videos and stuff like that. | [
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Policy update as of the trouble with the lab, not this week, but last week, your lowest two labs will now be dropped instead of just your lowest lab since AWS, I guess, killed our software right before the deadline. And then I just wanted to do a quick review because a couple of people that asked me about finding all the notes and videos and stuff like that. So if you go to Google, and if you can remember how to spell my name and type it, then you can find my homepage and then you can go down here to classes 120. | [
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And then I just wanted to do a quick review because a couple of people that asked me about finding all the notes and videos and stuff like that. So if you go to Google, and if you can remember how to spell my name and type it, then you can find my homepage and then you can go down here to classes 120. Oh, sorry, it still says 198 JL. That's the original name. F16, you go there and then on this links page, you have all the online exercises, you have all of the PowerPoint slides, have all of the recorded video lectures from the class, and then the C code examples and then some extra stuff if you want it. | [
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] |
That's the original name. F16, you go there and then on this links page, you have all the online exercises, you have all of the PowerPoint slides, have all of the recorded video lectures from the class, and then the C code examples and then some extra stuff if you want it. There's also a copy of the reading notes here. So if you're looking for those, they're here. Easier to read like this. | [
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So if you're looking for those, they're here. Easier to read like this. PowerPoint or PDF viewer doesn't want to do what I want right now. Anyway, so those are there. And then obviously the top thing takes you to the wiki where all the rest of the class resources are. So hopefully everyone knows how to find everything. So just do a quick review. There we go. All right, so today, oh now it's in, I look funny. | [
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There we go. All right, so today, oh now it's in, I look funny. I don't know why it went to that mode. Anyway, so we're gonna start by doing a checker for uppercase letters, more examples of building with abstraction, then talk about multiplexers or muxes, spend a little time on decoders. We may start sequential logic today or we may not get to it until Monday. I didn't put it on the list, but we may get there. | [
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We may start sequential logic today or we may not get to it until Monday. I didn't put it on the list, but we may get there. So I want to do another example and show you a few different ways that you can you can break up problems to make them easier than going all the way down to KMAPs. So let's start with one where we say, well let's have an ASCII character, 7-bit code, C, C6, down through C0. | [
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So I want to do another example and show you a few different ways that you can you can break up problems to make them easier than going all the way down to KMAPs. So let's start with one where we say, well let's have an ASCII character, 7-bit code, C, C6, down through C0. And let's make a piece of hardware that will tell us whether that ASCII character is an uppercase letter. So you may or may not remember an ASCII A is this bit pattern which is hex 41, capital Z is this bit pattern which is hex 5A. | [
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And let's make a piece of hardware that will tell us whether that ASCII character is an uppercase letter. So you may or may not remember an ASCII A is this bit pattern which is hex 41, capital Z is this bit pattern which is hex 5A. And so how do we check? If I give you this, these six or seven bits rather, how do you tell me is this a letter or not? Muhammad? Yeah, that's yeah, exactly. | [
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So you may or may not remember an ASCII A is this bit pattern which is hex 41, capital Z is this bit pattern which is hex 5A. And so how do we check? If I give you this, these six or seven bits rather, how do you tell me is this a letter or not? Muhammad? Yeah, that's yeah, exactly. That's one answer, right, is we can use some comparators. I'll put that off, I'll do it a slightly different way, but that's a good answer. | [
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That's one answer, right, is we can use some comparators. I'll put that off, I'll do it a slightly different way, but that's a good answer. Yeah, so these numbers here we're gonna have to feed into the comparator somehow, right? Yeah, good point. Okay, so we'll come back to that answer. So here's another way we can do it. Go down to truth table. Can you help me out? Is this one an ASCII character? No. | [
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] |
Go down to truth table. Can you help me out? Is this one an ASCII character? No. Okay, what about this one? Got a lot of slides here. So let's hurry up | [
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I'll put that off, I'll do it a slightly different way, but that's a good answer. Yeah, so these numbers here we're gonna have to feed into the comparator somehow, right? Yeah, good point. Okay, so we'll come back to that answer. So here's another way we can do it. Go down to truth table. Can you help me out? Is this one an ASCII character? No. Okay, what about this one? Got a lot of slides here. | [
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Can you help me out? Is this one an ASCII character? No. Okay, what about this one? Got a lot of slides here. So let's hurry up. All right, so maybe, maybe, I mean a lot of these are zero, right? Maybe we can just skip to the ones that matter. So what if we just take our truth table and we break it up into pieces? So we got 128 rows, but most of those rows are zero, right? So let's break it up into eight of them. | [
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All right, so maybe, maybe, I mean a lot of these are zero, right? Maybe we can just skip to the ones that matter. So what if we just take our truth table and we break it up into pieces? So we got 128 rows, but most of those rows are zero, right? So let's break it up into eight of them. So each of those eight pieces of 16 rows will be one value of C6, C5, and C4, right, the three leading bits. | [
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So what if we just take our truth table and we break it up into pieces? So we got 128 rows, but most of those rows are zero, right? So let's break it up into eight of them. So each of those eight pieces of 16 rows will be one value of C6, C5, and C4, right, the three leading bits. And then we can solve each of the little pieces, the groups of 16 rows, with a kmap on four variables, right? So we could do it that way. | [
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So each of those eight pieces of 16 rows will be one value of C6, C5, and C4, right, the three leading bits. And then we can solve each of the little pieces, the groups of 16 rows, with a kmap on four variables, right? So we could do it that way. So maybe we don't need a kmap for some of those, right? Maybe we don't need to do eight kmaps. So remember, A is this thing, Z is this thing. | [
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So maybe we don't need a kmap for some of those, right? Maybe we don't need to do eight kmaps. So remember, A is this thing, Z is this thing. So what about this truth table? So C6, C5, C4 equals 0, 0, 0. What's the function? Zero, right? So you didn't need a kmap, right? You want to draw a kmap? I know kmaps are fun, so maybe we do it. No, we'll just skip it. By the way, I want to make sure you know when I write something like this, this means C6 equals zero, and C5 equals zero, and C4 equals zero. | [
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No, we'll just skip it. By the way, I want to make sure you know when I write something like this, this means C6 equals zero, and C5 equals zero, and C4 equals zero. We'll write that increasingly often. So no ASCII character with those upper three bits is an uppercase letter, right? So that function is just zero. So that was relatively easy. So which of the eight functions are not the zero function? Yeah, so anytime we have C6, C5, C4 is 1, 0, 0, or 1, 0, 1, some of those are letters. | [
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So that was relatively easy. So which of the eight functions are not the zero function? Yeah, so anytime we have C6, C5, C4 is 1, 0, 0, or 1, 0, 1, some of those are letters. All the other possible values of those three bits, those are just the zero function, right? So out of eight different kmaps, six of them are zero. We're done, right? We've got two more. So if we break up the truth table, then we can solve a lot of it pretty quickly. | [
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We're done, right? We've got two more. So if we break up the truth table, then we can solve a lot of it pretty quickly. Well, six of them are zero. So let's call that function T4 before I'm getting out of just this number here, right? So 1, 0, 0 is four in decimal. We'll call this one T5, and that's it. So let's just do the kmaps for those two. So here's the kmap for T4. What do you think? SOP or POS? You want POS? Okay, the max term, right? So what is it? Yeah, add them all together, right? That one? Okay, okay, good. | [
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So here's the kmap for T4. What do you think? SOP or POS? You want POS? Okay, the max term, right? So what is it? Yeah, add them all together, right? That one? Okay, okay, good. We're done with T4. So it gets pretty easy at some point. Okay, so here's T5. I claim POS is slightly better again here. So what are the loops? Yeah, I want to do POS again. Yeah, sorry | [
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So here's the kmap for T4. What do you think? SOP or POS? You want POS? Okay, the max term, right? So what is it? Yeah, add them all together, right? That one? Okay, okay, good. We're done with T4. So it gets pretty easy at some point. Okay, so here's T5. I claim POS is slightly better again here. So what are the loops? Yeah, I want to do POS again. Yeah, sorry. So this one here? Okay, good. | [
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Yeah, sorry. So this one here? Okay, good. What is that one? Like that? Okay, and what's the other? The two horizontal zeros? Okay, and that one's this? Good, okay. So that's it, right? Those two factors. All right, so then how do we put them together? So we've got T4, we've got T5 with six zeros. We could write down if we want. I won't write them. So T4 applies when C6, C5, C4 is 1, 0, 0. | [
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I won't write them. So T4 applies when C6, C5, C4 is 1, 0, 0. T5 applies when C6, C5, C4 is 1, 0, 1. So what should I do? All right, so what if I, let's see, so I want this one to apply when this is true. Can I write an expression for this? So I need to AND T4 with C6, C5 prime, C4 prime, right? So if I write C6, C5 prime, C4 prime, that means these three are equal to those three. Is that right? Okay. | [
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Can I write an expression for this? So I need to AND T4 with C6, C5 prime, C4 prime, right? So if I write C6, C5 prime, C4 prime, that means these three are equal to those three. Is that right? Okay. So AND T4 with C6, C5 prime, C4 prime, AND T5 with what? C6, C5 prime, C4, okay. And then do what with those two results? OR them together, right? Good. Okay. So that's my answer. So it looks nasty, but it's not really that bad, right? It's pretty small, pretty fast. | [
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So that's my answer. So it looks nasty, but it's not really that bad, right? It's pretty small, pretty fast. It's not two-level logic. It's a little more, but we still had to do a little bit of work, right? So you already know the easier way. So this is the question we can think of it as, right? We know how to build comparators. So instead of saying, let's go build this expression, we can instead say, well, I know how to build a comparator. | [
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So this is the question we can think of it as, right? We know how to build comparators. So instead of saying, let's go build this expression, we can instead say, well, I know how to build a comparator. I know this is a contiguous range because on homework number one, we asked you some question about why did we put digits in a contiguous range? And you said, well, so you could do translation to binary numbers, right? And well, why do we put letters in a contiguous range? So you could do this kind of thing. | [
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So instead of saying, let's go build this expression, we can instead say, well, I know how to build a comparator. I know this is a contiguous range because on homework number one, we asked you some question about why did we put digits in a contiguous range? And you said, well, so you could do translation to binary numbers, right? And well, why do we put letters in a contiguous range? So you could do this kind of thing. So you need to check, well, is C greater or equal than A and less or equal than Z? If it is, well, then it's a letter. | [
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] |
I know this is a contiguous range because on homework number one, we asked you some question about why did we put digits in a contiguous range? And you said, well, so you could do translation to binary numbers, right? And well, why do we put letters in a contiguous range? So you could do this kind of thing. So you need to check, well, is C greater or equal than A and less or equal than Z? If it is, well, then it's a letter. And if it's not, it's not an uppercase letter. | [
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] |
So you need to check, well, is C greater or equal than A and less or equal than Z? If it is, well, then it's a letter. And if it's not, it's not an uppercase letter. So here's two comparators. So I built two seven-bit comparators using our bit-slice approach and just plopped them down in my diagram. Into both A inputs, I put the C, the character in ASCII that we're comparing. Into the left comparator, I'm going to put hex 41. | [
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] |
Into both A inputs, I put the C, the character in ASCII that we're comparing. Into the left comparator, I'm going to put hex 41. That's the letter A, remember? And the right comparator, I'm going to put the letter Z. That's 5A | [
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And if it's not, it's not an uppercase letter. So here's two comparators. So I built two seven-bit comparators using our bit-slice approach and just plopped them down in my diagram. Into both A inputs, I put the C, the character in ASCII that we're comparing. Into the left comparator, I'm going to put hex 41. That's the letter A, remember? And the right comparator, I'm going to put the letter Z. | [
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] |
Into the left comparator, I'm going to put hex 41. That's the letter A, remember? And the right comparator, I'm going to put the letter Z. That's 5A. And then I have to go back and look at my representation, which I didn't rewrite for you guys. But remember that if you've got Z0 on, that implies that C is actually less than 41 hex. That A is less than B. The Z0 output is 1. And if the Z1 output is 1, that implies that the A is greater than B. | [
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The Z0 output is 1. And if the Z1 output is 1, that implies that the A is greater than B. So C is greater than 5A. So if either of those conditions are true, it's not an uppercase letter. So if C is less than the letter A, then it's not an uppercase letter. Or if it's greater than the letter Z, it's also not an uppercase letter. So I have a NOR gate down here that takes those two NORs them together and gives us our uppercase function. | [
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Or if it's greater than the letter Z, it's also not an uppercase letter. So I have a NOR gate down here that takes those two NORs them together and gives us our uppercase function. So fairly simple, fairly easy. Probably could write it down in a couple of minutes. The hard part is going back and looking at the representation to figure out what gate to put there. OK. What about this? So you know how to build adders, right? You could do it with adders. | [
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OK. What about this? So you know how to build adders, right? You could do it with adders. So last lecture, we saw how to build subtractors. So these are actually being used as subtractors, right? So this thing here, so what's BE for? Well, that's 41 hex, one's complement form. And so this is one's complement of 41. This is carry in of one. Remember that when we take C, this is 0 extended to be 8 bits. | [
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This is carry in of one. Remember that when we take C, this is 0 extended to be 8 bits. When we take C and we add it to not be plus 1, that gives us C minus 41. So C minus 41, if that overflows, I'm sorry, yeah, if we get the carry out, that means no overflow. If we don't have a carry out, if carry out is 0, that means that C was less than 41 hex. So if we get a 0 carry out that comes down here, goes through an inverter, changes to a 1, forces you to 0. | [
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If we don't have a carry out, if carry out is 0, that means that C was less than 41 hex. So if we get a 0 carry out that comes down here, goes through an inverter, changes to a 1, forces you to 0. So in other words, if C is less than letter A, capital letter A, we'll get a U of 0. Similarly over here, A4 is one's complement of 5A, I think. I put that wrong, didn't I? It should be A5. | [
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Similarly over here, A4 is one's complement of 5A, I think. I put that wrong, didn't I? It should be A5. Sorry about that. So that should be A5. Yeah. Oh, wait, do we need a, let me think here. So we get this one minus 5A, maybe it's for the greater or equal. So 5A, yeah, it's inverted sense. So this is C minus 5B. And so if we get a carry out of that, it's 5B or more. So that's why it's off by 1 here. | [
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And so if we get a carry out of that, it's 5B or more. So that's why it's off by 1 here. So this has to be the greater or equal to 5B. That's what the carry out means. If that's true, it's not an uppercase letter. So we're getting a greater or equal then when we flip the carry sense | [
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So 5A, yeah, it's inverted sense. So this is C minus 5B. And so if we get a carry out of that, it's 5B or more. So that's why it's off by 1 here. So this has to be the greater or equal to 5B. That's what the carry out means. If that's true, it's not an uppercase letter. So we're getting a greater or equal then when we flip the carry sense. And that's why this is one's complement of 5B instead of 5A. | [
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So we're getting a greater or equal then when we flip the carry sense. And that's why this is one's complement of 5B instead of 5A. Does that make sense? OK. All right. So with these two adders, so basically each adder is checking one bound of the range, same as with the comparators. So we could build it this way too and get the same answer. So what's the trade off? Well, those are kind of large and slow compared to our first solution. | [
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So we could build it this way too and get the same answer. So what's the trade off? Well, those are kind of large and slow compared to our first solution. If you write it down as gates and you show how many gates you need for that first expression, it's really not very many. It's pretty fast, a few levels of logic. As compared to our 7-bit comparator, where it's going to have maybe order 14, 15, plus the logic at the end, so 16 or so gate delays. | [
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It's pretty fast, a few levels of logic. As compared to our 7-bit comparator, where it's going to have maybe order 14, 15, plus the logic at the end, so 16 or so gate delays. So substantially slower, substantially bigger for the comparator approach. Same thing for the adders. You've got to wait for the carries to ripple through if you build them as ripple carry adders. So they're slower and bigger. | [
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You've got to wait for the carries to ripple through if you build them as ripple carry adders. So they're slower and bigger. On the other hand, the CAD tools can optimize a lot of that overhead away. So if you look back at the adders, we're actually throwing away the sums. So we build these adders and then we calculate the sum and then we just ignore it. So the CAD tools can look at that and say, well, you didn't use those. | [
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So we build these adders and then we calculate the sum and then we just ignore it. So the CAD tools can look at that and say, well, you didn't use those. So any gates I use to generate those bits, I don't need those. And so it already start trimming down the design that way. But it can also do a little bit of optimization for you. The other way to look at this is, this is like XML parsing or something. | [
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But it can also do a little bit of optimization for you. The other way to look at this is, this is like XML parsing or something. If you're going to do XML parsing in your data center, which lots of data centers are doing 24 hours a day, seven days a week, 365 days a year all the time, what are those doing? Well, they're using software. They're saying, oh, compare this incoming character to capital A, compare it to capital Z, actually probably with 32 or 64 bits at a time instead of eight bits. | [
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If you're going to do XML parsing in your data center, which lots of data centers are doing 24 hours a day, seven days a week, 365 days a year all the time, what are those doing? Well, they're using software. They're saying, oh, compare this incoming character to capital A, compare it to capital Z, actually probably with 32 or 64 bits at a time instead of eight bits. So we're actually doing that all the time in much less efficient ways in software. | [
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They're saying, oh, compare this incoming character to capital A, compare it to capital Z, actually probably with 32 or 64 bits at a time instead of eight bits. So we're actually doing that all the time in much less efficient ways in software. So this kind of hardware, if you build something like this and if you can get it sitting and doing XML processing, for example, it's more of a complicated task than just checking characters. | [
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So we're actually doing that all the time in much less efficient ways in software. So this kind of hardware, if you build something like this and if you can get it sitting and doing XML processing, for example, it's more of a complicated task than just checking characters. But it can actually be a lot faster even with a slower and bigger design than using processors. Yeah. Yeah, possibly. | [
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Yeah. Yeah, possibly. And that would be an argument for doing it in software. The computers you're using in software are part of the processor and you can use them for myriad other purposes. But in reality, even 15, 20 years ago with TCP IP network processing before everything was XML based or HTML based, if you looked at a typical data center, a lot of your processor cycles, so on the order of 10 to 15% of your processor cycles were spent doing this stuff. | [
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The computers you're using in software are part of the processor and you can use them for myriad other purposes. But in reality, even 15, 20 years ago with TCP IP network processing before everything was XML based or HTML based, if you looked at a typical data center, a lot of your processor cycles, so on the order of 10 to 15% of your processor cycles were spent doing this stuff | [
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Yeah. Yeah, possibly. And that would be an argument for doing it in software. The computers you're using in software are part of the processor and you can use them for myriad other purposes. But in reality, even 15, 20 years ago with TCP IP network processing before everything was XML based or HTML based, if you looked at a typical data center, a lot of your processor cycles, so on the order of 10 to 15% of your processor cycles were spent doing this stuff. | [
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The computers you're using in software are part of the processor and you can use them for myriad other purposes. But in reality, even 15, 20 years ago with TCP IP network processing before everything was XML based or HTML based, if you looked at a typical data center, a lot of your processor cycles, so on the order of 10 to 15% of your processor cycles were spent doing this stuff. So there's actually a reasonable amount of research in what people call TCP offloading, try to process networking protocols, TCP IP offloading, networking protocols in hardware off the main processors so that you could have your processors actually run internet services instead and reduce your costs that way. | [
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But in reality, even 15, 20 years ago with TCP IP network processing before everything was XML based or HTML based, if you looked at a typical data center, a lot of your processor cycles, so on the order of 10 to 15% of your processor cycles were spent doing this stuff. So there's actually a reasonable amount of research in what people call TCP offloading, try to process networking protocols, TCP IP offloading, networking protocols in hardware off the main processors so that you could have your processors actually run internet services instead and reduce your costs that way. So yes and no. | [
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So there's actually a reasonable amount of research in what people call TCP offloading, try to process networking protocols, TCP IP offloading, networking protocols in hardware off the main processors so that you could have your processors actually run internet services instead and reduce your costs that way. So yes and no. There's benefit to it, but getting the generality you need, especially as the protocols evolve over time is sometimes difficult. | [
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So yes and no. There's benefit to it, but getting the generality you need, especially as the protocols evolve over time is sometimes difficult. So people have tried the TCP IP networking at least three times in the last 30 years. And there's some of it now I think in the industry and in real data centers. But it's hard to get right in a way that can survive for a long time. And that's partly because once you put it in hardware, you can't change it. | [
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But it's hard to get right in a way that can survive for a long time. And that's partly because once you put it in hardware, you can't change it. It has to be the same. Good question. Yeah. I'm not in this class, but you can do it. Good question. Yeah. Yeah. I wouldn't ask you to do something that complicated in our class. But yeah. So we want you to understand how to do it and how to approach these kind of problems, both in the sense of if you want to go down to the level of building out of gates to know how to do those things, but also to know how to use the components that you can pull off the shelf to build things. | [
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But yeah. So we want you to understand how to do it and how to approach these kind of problems, both in the sense of if you want to go down to the level of building out of gates to know how to do those things, but also to know how to use the components that you can pull off the shelf to build things. So right now we're looking at examples of the latter. To solve problems, you can take pieces of known solutions and glue them together and do that very, very quickly and only optimize afterwards. | [
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So right now we're looking at examples of the latter. To solve problems, you can take pieces of known solutions and glue them together and do that very, very quickly and only optimize afterwards. If it's something that is too slow or too big, then you can go make it smaller and faster by spending more time on it. So we want you to understand both strategies. Does that answer the question? Okay. | [
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So we want you to understand both strategies. Does that answer the question? Okay. Another question? Okay. Yeah. Can you look ahead in my slides? Yes. Yes, we can. Hold that thought. I won't repeat it for the camera because it'll come up again. Good question. Anything else? Okay. So multiplexers. So here we go. You didn't have to hold it for long. So what if we want to take a lowercase letter? So lowercase letters are 61 hex through 7a hex. | [
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You didn't have to hold it for long. So what if we want to take a lowercase letter? So lowercase letters are 61 hex through 7a hex. Remember that uppercase or 41 through 5a. So can we reuse our solutions? We just do what? What was it you said? That? Right. So you'll notice if you put them side by side that bit c5 is flipped. Right. So I'm sorry. I took down the representations, but they couldn't all fit on the slides. | [
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So I'm sorry. I took down the representations, but they couldn't all fit on the slides. We had this answer before by breaking up the truth table. So I'll go back. The only difference here is bit c5 here is a 1, bit c5 here is a 0, c5 is a 1, c5 is a 0. Right. So flip the c5. So change c5 here, c5 here to c5, sorry, c5 prime, c5 prime to c5 c5. We're done. We've got a lowercase checker. | [
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] |
We're done. We've got a lowercase checker. Yeah. Oh, sorry. I thought you were raising your hand. Okay | [
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So I'll go back. The only difference here is bit c5 here is a 1, bit c5 here is a 0, c5 is a 1, c5 is a 0. Right. So flip the c5. So change c5 here, c5 here to c5, sorry, c5 prime, c5 prime to c5 c5. We're done. We've got a lowercase checker. Yeah. Oh, sorry. I thought you were raising your hand. Okay. And if you want to use the comparator for that purpose, right, then all you have to do is change these inputs up here. | [
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Okay. And if you want to use the comparator for that purpose, right, then all you have to do is change these inputs up here. So change that one from 41 to 61. That means z0 equals 1 now implies c less than 61 hex. Change this one from 5a to 7a. That means that z1 down here equals 1 implies c greater than 7a instead of 5a. And then we have a lowercase checker instead of an uppercase checker. | [
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That means that z1 down here equals 1 implies c greater than 7a instead of 5a. And then we have a lowercase checker instead of an uppercase checker. So very, very easy to just go change that answer. So what if we want to design one answer to one piece of hardware that does both? So we did that a couple of times on Wednesday. We did unsigned and choose complement comparator by XORing the sign bits with the signal s. | [
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So what if we want to design one answer to one piece of hardware that does both? So we did that a couple of times on Wednesday. We did unsigned and choose complement comparator by XORing the sign bits with the signal s. We did that with an adder and subtractor where we put them together by again having control signal s. But what if we want to have just logic that allows us to have some control signal s that just selects between two arbitrary signals? So we'll design this logic and then go apply it to our problem here of designing one piece of hardware that checks both upper and lowercase. | [
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We did that with an adder and subtractor where we put them together by again having control signal s. But what if we want to have just logic that allows us to have some control signal s that just selects between two arbitrary signals? So we'll design this logic and then go apply it to our problem here of designing one piece of hardware that checks both upper and lowercase. So if I want to do that, here's a full truth table. | [
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But what if we want to have just logic that allows us to have some control signal s that just selects between two arbitrary signals? So we'll design this logic and then go apply it to our problem here of designing one piece of hardware that checks both upper and lowercase. So if I want to do that, here's a full truth table. So I have a select bit s. It could be 0 or 1. I have two data inputs. | [
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It could be 0 or 1. I have two data inputs. They could be 0 or 1. And those are the eight possible patterns. And so if I have select bit 0, that pulls out d0 and I get a 0, 0, 1, 1, 0, 0, so forth. But I could probably make it a little shorter. So instead of drawing this big truth table, I know that if I select 0, I don't care what d1 is. So here we're putting X on an input, which is different than putting X on an output. | [
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So instead of drawing this big truth table, I know that if I select 0, I don't care what d1 is. So here we're putting X on an input, which is different than putting X on an output. This says in this truth table row, d1 doesn't matter. d1 can be 0 or 1, and Q will still be 0. So this row here then represents these top two, I'm sorry, not the top two, this one and this one here, the first and the third. | [
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d1 can be 0 or 1, and Q will still be 0. So this row here then represents these top two, I'm sorry, not the top two, this one and this one here, the first and the third. The second row then represents the second and the fourth. It also says, well, if select is 0, d1 doesn't matter. If d0 is 1, Q is also 1. So we can have an abbreviated truth table. I mostly wanted to show you what it means to have a don't care symbol on the inputs. | [
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So we can have an abbreviated truth table. I mostly wanted to show you what it means to have a don't care symbol on the inputs. So it means that we're merging multiple lines with the same output. You have to be careful because if you have more than one overlapping set here in your rows with different outputs, then you have an ill-defined truth table. So you've got to be careful how you merge them. | [
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