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All right, so but usually it's probably worthwhile. So how can we build gates? So the first thing we did is we said, well, we've got electrons. We can measure voltages. Give us a bit, right, binary digit. Then we said, well, let's look at representations based on bits, based on electrons here and there. Then we said, OK, we can do functions on bits with Boolean algebra. But we kind of skipped over the device level. | [
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Then we said, OK, we can do functions on bits with Boolean algebra. But we kind of skipped over the device level. So today we're going to start looking at, well, how do you take devices like CMOS transistors? I'll tell you what CMOS means later. I'm sorry, CMOS gates, MOSFET transistors, and build these Boolean functions out of them. So that's what we're going to start looking at today. | [
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I'm sorry, CMOS gates, MOSFET transistors, and build these Boolean functions out of them. So that's what we're going to start looking at today. But first, I want to run something by you. This is just so exciting. I had a really great idea. They call it a torch. Just point it at you, and it'll light you up. It'll be so nice. You can point it at the podium. It'll light up. No, just it's a light. | [
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It'll light up. No, just it's a light. I mean, you see, it's a lamp. It's not a laser. Actually, Nick Coloniak gave a talk, and he had a visible light LED that was still under the danger level. But you didn't know that when he said, see, look how bright it is. And he said, oh, don't worry. It's safe. Thanks, Nick. So good idea? What do you think? What? But you want me to do what? Like this? But people already make those. | [
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Thanks, Nick. So good idea? What do you think? What? But you want me to do what? Like this? But people already make those. I can't patent that. They call it a flashlight. You've never seen this? All right. I don't know. All right, I had another idea. Here's another idea. You like switches? A bunch of switches together. A lot of switches. It'd be good. How many of you play video games? See, this will be great. | [
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It'd be good. How many of you play video games? See, this will be great. Good exercise for you. And when you want to change your bid, you just flip a switch. Be the hand-operated computer. Sound good? Good idea? Yeah? OK, we're going to do that? OK, you don't like that. I know some of you didn't like it. Some of you liked it. I got to say, if you want to be a video game champion, it's all in the training. | [
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Some of you liked it. I got to say, if you want to be a video game champion, it's all in the training. So if you don't want to do the hand-operated computer, I understand. But we do a voltage-controlled switch. Then one switch can control another switch. And that switch can control another switch. So we can put two billion switches all together in one circuit. So that's a really cool idea. | [
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So we can put two billion switches all together in one circuit. So that's a really cool idea. I'm getting tired just thinking about that thumb thing. Let's take a little break. So the person who invented that cool idea a long time ago, 70 years ago almost, John Bardeen and Shockley and Bertain. One of them's a manager, but you can read about that if you want | [
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But we do a voltage-controlled switch. Then one switch can control another switch. And that switch can control another switch. So we can put two billion switches all together in one circuit. So that's a really cool idea. I'm getting tired just thinking about that thumb thing. Let's take a little break. So the person who invented that cool idea a long time ago, 70 years ago almost, John Bardeen and Shockley and Bertain. | [
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Let's take a little break. So the person who invented that cool idea a long time ago, 70 years ago almost, John Bardeen and Shockley and Bertain. One of them's a manager, but you can read about that if you want. But they invented it at Bell Labs. Four years later, John Bardeen joined our faculty, also the physics faculty here. Got a Nobel Prize a few years later. After that, maybe another 16 years, they got a second Nobel Prize for BCS theory of superconductivity. | [
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Got a Nobel Prize a few years later. After that, maybe another 16 years, they got a second Nobel Prize for BCS theory of superconductivity. This is where electrons pair up and act like bosons, allowing them to move without bumping into things. His first PhD student then, Nick Koloniak, invented things like the visible light LED. So all the lighting you see all over the world basically stems back to one of our faculty members, Nick Koloniak, who I mentioned a few minutes ago. | [
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His first PhD student then, Nick Koloniak, invented things like the visible light LED. So all the lighting you see all over the world basically stems back to one of our faculty members, Nick Koloniak, who I mentioned a few minutes ago. He also invented things like laser diodes for CDs and DVDs, if you have ever used those, and dimmer switches and other things like that. Here are some of the things that he was awarded. | [
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He also invented things like laser diodes for CDs and DVDs, if you have ever used those, and dimmer switches and other things like that. Here are some of the things that he was awarded. You can find a much longer list on the web if you want to look. Nick's first student, I think it was his first student, Greg Stillman, also joined the ECE faculty, invented things like avalanche photodiodes, elected to the National Academy of Engineering. | [
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] |
You can find a much longer list on the web if you want to look. Nick's first student, I think it was his first student, Greg Stillman, also joined the ECE faculty, invented things like avalanche photodiodes, elected to the National Academy of Engineering. This is actually the most prestigious honor for an engineer in the US. It's basically being called to serve the country as an advisor, as an engineer. | [
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This is actually the most prestigious honor for an engineer in the US. It's basically being called to serve the country as an advisor, as an engineer. He founded the MNTL lab, which is just right next to us, and was its first director. His first student, Milton Fang, also joined the ECE faculty and burned the terahertz transistors. So very, very fast, much faster than your typical computer these days. | [
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His first student, Milton Fang, also joined the ECE faculty and burned the terahertz transistors. So very, very fast, much faster than your typical computer these days. Also the light emitting transistor, both of these were done with Nick Koloniak and the transistor laser. And he just retired actually this fall. So you could have worked with him had you come last year. Actually, he's still around doing research. | [
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So you could have worked with him had you come last year. Actually, he's still around doing research. But not just faculty, so just to mention one of our students, how many of you are going to get a BSEE? The others are BSEE, right? OK, people don't want to raise their hands today. I know we've got more E's than that. Anyway, so but now you're feeling shy because I'm putting Kilby up there. | [
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] |
I know we've got more E's than that. Anyway, so but now you're feeling shy because I'm putting Kilby up there. All right, so he got his BSEE in 1947. 10 years or so later, he invented the integrated circuit at Texas Instruments. He also invented things like the thermal printer and the handheld calculator, National Academy of Engineering, and of course, Nobel Prize for physics. So now you know why we expect a lot of you. | [
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He also invented things like the thermal printer and the handheld calculator, National Academy of Engineering, and of course, Nobel Prize for physics. So now you know why we expect a lot of you. Yes. Yeah, seriously. I'm not kidding. OK, so all right, so that was just a little bragging break so you know more about Illinois history. So digital electronics today is based on MOSFET. So what's a MOSFET? The material is metal oxide semiconductor and the technology is a field effect transistor. | [
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So digital electronics today is based on MOSFET. So what's a MOSFET? The material is metal oxide semiconductor and the technology is a field effect transistor. So the voltage basically turns the transistor on and off. It's a voltage controlled switch. So there are two kinds which are named after the charge carrier. So there are electrons | [
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Yes. Yeah, seriously. I'm not kidding. OK, so all right, so that was just a little bragging break so you know more about Illinois history. So digital electronics today is based on MOSFET. So what's a MOSFET? The material is metal oxide semiconductor and the technology is a field effect transistor. So the voltage basically turns the transistor on and off. It's a voltage controlled switch. | [
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So the voltage basically turns the transistor on and off. It's a voltage controlled switch. So there are two kinds which are named after the charge carrier. So there are electrons. So if the electrons move, it's called a negative type. And if the absence of electrons, which we call holes, move, it's called a positive type. I think not too many of you have taken quantum mechanics, right? So a few of you. | [
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And if the absence of electrons, which we call holes, move, it's called a positive type. I think not too many of you have taken quantum mechanics, right? So a few of you. So if you think back to, I think probably most of you have high school chemistry. So if you think about what happens when you have valence electrons, you can put two in the same orbital, and one is spin up and one is spin down. | [
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So if you think back to, I think probably most of you have high school chemistry. So if you think about what happens when you have valence electrons, you can put two in the same orbital, and one is spin up and one is spin down. And if you have one absence, then it acts kind of like a positive charge. And if you have an extra one in your orbital, it acts like a negative charge. So it's the same sort of idea that in semiconductors, you have energy states. | [
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And if you have an extra one in your orbital, it acts like a negative charge. So it's the same sort of idea that in semiconductors, you have energy states. And if some of the energy states are empty, they act like holes. So if the holes are moving around, it's a p-type. If the electrons are moving around, it's an n-type. Just a way to remember p and n, positive or negative charge carrier. | [
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If the electrons are moving around, it's an n-type. Just a way to remember p and n, positive or negative charge carrier. So how do these things work? You can learn a lot more in EC 440, I guess 340 now, if you want to take that class later. But I guess all the EEs will probably take it. But CompE is an elective. So an n-type MOSFET turns on when the voltage between the gate on the left here and the other terminals, it's a symmetric device. | [
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] |
But CompE is an elective. So an n-type MOSFET turns on when the voltage between the gate on the left here and the other terminals, it's a symmetric device. But between the gate and the other terminals exceeds a threshold. So if the voltage is smaller, the transistor turns off. And then current cannot flow between the other two terminals. Historically, they were called source and drain. | [
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And then current cannot flow between the other two terminals. Historically, they were called source and drain. But that implies a direction. And this, again, is a symmetric device. So we need two voltages. We're going to do binary digital systems. So we need a ground. And that's our binary 0 value. And we need a VDD, which today is about 1 and 1 half volts. That's our high voltage, our binary 1. | [
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And we need a VDD, which today is about 1 and 1 half volts. That's our high voltage, our binary 1. It used to be about 5 volts. Actually, the stuff you'll play with in the lab in maybe about five to seven weeks will be 5-volt TTL chips. But on modern processors, it's usually about a volt and a half. So we can use these binary voltages to control, say, an n-type MOSFET. Now, remember, it only will turn on when the gate voltage is high. | [
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] |
So we can use these binary voltages to control, say, an n-type MOSFET. Now, remember, it only will turn on when the gate voltage is high. So the voltage has to exceed a threshold. So if we put 1.5 volts, and then one of the other terminals has 0 volts, as you see on the left here, the current can flow. And then the top terminal can get pulled down to 0 volts. So to turn on an n-type MOSFET, you put high voltage, binary 1 in, on the gate. | [
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] |
And then the top terminal can get pulled down to 0 volts. So to turn on an n-type MOSFET, you put high voltage, binary 1 in, on the gate. And then if you have one of these connected to ground, then the other side will come down to ground as well, because the transistor will turn on. This is circuit terminology. You say the circuit's closed or open | [
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And then the top terminal can get pulled down to 0 volts. So to turn on an n-type MOSFET, you put high voltage, binary 1 in, on the gate. And then if you have one of these connected to ground, then the other side will come down to ground as well, because the transistor will turn on. This is circuit terminology. You say the circuit's closed or open. I'd prefer to say on and off. I find it less confusing. | [
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I'd prefer to say on and off. I find it less confusing. But either one is fine. So this one, when we put 0 volts on the input, remember that in our binary voltage system, the full range of voltage is only 0 to 1.5. So you can't have anything lower than 0 over here. And so you can't exceed the threshold. So essentially, whenever you put a 0 onto the gate of the n-type MOSFET, it will turn itself off. | [
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And so you can't exceed the threshold. So essentially, whenever you put a 0 onto the gate of the n-type MOSFET, it will turn itself off. So p-type MOSFET, the voltage goes the other direction. So if the voltage from these terminals on the right to the gate terminal exceeds a threshold, then the p-type will turn on, which means current can flow between the two terminals on the right. | [
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] |
So p-type MOSFET, the voltage goes the other direction. So if the voltage from these terminals on the right to the gate terminal exceeds a threshold, then the p-type will turn on, which means current can flow between the two terminals on the right. And if the voltage is smaller, it turns off. So the voltage just goes the other direction. So here's the same diagram with the p-type. So in order to turn it on, we need to put our ground voltage in on the gate. | [
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] |
So here's the same diagram with the p-type. So in order to turn it on, we need to put our ground voltage in on the gate. You'll notice, by the way, that there's this inverter bubble thing here on the p-type. I'll explain how that will help you. Remember which one is n-type and which one is p-type and how they work in a minute. But if you put 0 volts on the gate and you have high voltage on one of the terminals, the p-type transistor will turn on. | [
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] |
Remember which one is n-type and which one is p-type and how they work in a minute. But if you put 0 volts on the gate and you have high voltage on one of the terminals, the p-type transistor will turn on. And this high voltage can pull this terminal up to high voltage as well. If, on the other hand, you put high voltage on the gate, then you're not going to have any current. Remember that the whole range of voltages here is 0 to 1. | [
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If, on the other hand, you put high voltage on the gate, then you're not going to have any current. Remember that the whole range of voltages here is 0 to 1.5 volts. And so you can't get a higher voltage here to turn the transistor on. And so the p-type will always be off if you put 1.5 or a binary 1 on its gate. Yeah? So that's when? Yeah, so as soon as you get a voltage with the p-type, if the voltage from this point to that point is greater than a threshold, and the threshold is, say, about 70% or 80% of the high voltage, so maybe 1. | [
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5 or a binary 1 on its gate. Yeah? So that's when? Yeah, so as soon as you get a voltage with the p-type, if the voltage from this point to that point is greater than a threshold, and the threshold is, say, about 70% or 80% of the high voltage, so maybe 1.2, 1.3 volts. So if the voltage difference is sufficient, then this acts like a wire between the two terminals, just like down here. | [
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3 volts. So if the voltage difference is sufficient, then this acts like a wire between the two terminals, just like down here. And if the voltage difference is below that threshold, which it always will be if you put high voltage on the gate, then it acts like an open switch. It's turned off. You will not learn. This is the level of detail we'll cover in the class. The question is, will you see PNP junctions? If you want to learn more about transistors, then 340 is the class. | [
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This is the level of detail we'll cover in the class. The question is, will you see PNP junctions? If you want to learn more about transistors, then 340 is the class. So they'll cover semiconductor devices, basically, and give you a lot of detail on this. You'll see a little bit more. You'll see an ID curve, current versus voltage curve, in 110. So you'll see a tiny bit more in 110. | [
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You'll see an ID curve, current versus voltage curve, in 110. So you'll see a tiny bit more in 110. OK, so the drawings will actually help you remember how they work | [
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This is the level of detail we'll cover in the class. The question is, will you see PNP junctions? If you want to learn more about transistors, then 340 is the class. So they'll cover semiconductor devices, basically, and give you a lot of detail on this. You'll see a little bit more. You'll see an ID curve, current versus voltage curve, in 110. So you'll see a tiny bit more in 110. OK, so the drawings will actually help you remember how they work. | [
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So you'll see a tiny bit more in 110. OK, so the drawings will actually help you remember how they work. So you notice on the p-type, we have this inverter bubble on the gate. So you should just remember that that means if you put a 0, it turns on, whereas the n-type, you don't have the inverter bubble, the little circle. So n-type turns on if you put a 1 on the gate. P-type turns on if you put a 0 on the gate. | [
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So n-type turns on if you put a 1 on the gate. P-type turns on if you put a 0 on the gate. Might not be so helpful to remember the names, because at least for me, they're sort of opposite of the binary digits that you'd put onto them to make them work, because they refer to the charge carriers. Yeah? Yes, this is an illustration of the on and off of p-type. And two slides back was on and off of n-type. | [
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Yeah? Yes, this is an illustration of the on and off of p-type. And two slides back was on and off of n-type. OK, so how do we actually build gates? So to build gates, we're going to use what are called complementary structures of p-type and n-type MOSFETs. So we'll have an equal number of each type of MOSFET. On the top, we'll put our p-types. The bottom, we'll put our n-types. We say that digital systems are based on CMOS, complementary MOS. | [
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The bottom, we'll put our n-types. We say that digital systems are based on CMOS, complementary MOS. So pretty much every digital system you'll see, except for some high-speed networking equipment, will be based on CMOS. So all of your cell phones, all of your computers, most network routers. What does this gate do? So here's the simplest one. We put one p-type on top, one n-type on the bottom. | [
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What does this gate do? So here's the simplest one. We put one p-type on top, one n-type on the bottom. What does it do? So let's go through and analyze it. So let's start. Write a truth table. So first, we'll put in voltages, and then we'll change them later to 0s and 1s. So start with a equals 0 volts. So what about the top transistor, on or off? It'll be on, right? p-type has a 0 volts on the gate, so that'll be on. | [
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] |
So start with a equals 0 volts. So what about the top transistor, on or off? It'll be on, right? p-type has a 0 volts on the gate, so that'll be on. What about the bottom one? Off. OK, so now we have basically a connection going from Q, the output, up to VDD. So now, remember I said, well, if one of the terminals is at 1.5 volts and the gate's at 0, it can pull the other one up. So this will pull the output up to 1. | [
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5 volts and the gate's at 0, it can pull the other one up. So this will pull the output up to 1.5 volts. We'll write that in the truth table. What about the other case? So if A is 1.5 volts, we put the labels on. Top transistor? Off. Bottom transistor? On. Good. So now we have a path down to ground. So here, the n-type is pulling Q down to ground, down to 0 volts, by just connecting it through its two terminals, because its gate input is 1. | [
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] |
So now we have a path down to ground. So here, the n-type is pulling Q down to ground, down to 0 volts, by just connecting it through its two terminals, because its gate input is 1.5 volts. So it's 0 volts. So now let's convert those voltages into our binary values. We get those. So it's a NOT gate, right? Yeah. No. I'll just throw it | [
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Top transistor? Off. Bottom transistor? On. Good. So now we have a path down to ground. So here, the n-type is pulling Q down to ground, down to 0 volts, by just connecting it through its two terminals, because its gate input is 1.5 volts. So it's 0 volts. So now let's convert those voltages into our binary values. We get those. So it's a NOT gate, right? Yeah. No. I'll just throw it. | [
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No. I'll just throw it. So you'll see the bottom transistor is on. Top one's off. So the bottom transistor acts as a wire. So now this is ground down here, this little triangle. Sorry. Yeah. So it's changing? Yeah, it's connecting the output Q to ground, when you put A as 1.5 volts under these two transistors. The top one turns off. The bottom one turns on. Creates a wire to ground. | [
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The bottom one turns on. Creates a wire to ground. Yeah. Yeah, so the p-type MOSFET, so it's not a gate. This whole thing is a gate. But the p-type MOSFET has the circle on the input. MOSFET is metal oxide semiconductor field effect transistor. You don't really need to know. Yeah, transistor. Good answer. Yeah. OK. All right. Yeah, we won't quiz you on that. Although I used to give out candy when teaching the networking classes. | [
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Yeah, we won't quiz you on that. Although I used to give out candy when teaching the networking classes. There's so many TLAs. Because no TLA, right? Yeah, good. Three letter acronym, exactly. There's so many TLAs that I told my networking class, well, if I give you an acronym and you challenge me and I can't tell you what it means, I'll give everyone in the room candy. And they actually got me a couple of times. | [
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There's so many TLAs that I told my networking class, well, if I give you an acronym and you challenge me and I can't tell you what it means, I'll give everyone in the room candy. And they actually got me a couple of times. It was fairly embarrassing. I'll give you the same deal, because I shouldn't do that to you either. But you have to remember. I won't remind you. Yeah. Yes, yes. | [
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Yeah. Yes, yes. So this thing down at the bottom is a general symbol for ground. Yes. And this up here is a general symbol for high voltage. So ground, high voltage. Yeah, this up here is high voltage. And this is ground. Yeah, sorry. Forgot, you might not have seen those. OK. So that's our NOT gate. And of course, we draw it like that. This is how we actually implement an inverter with two MOSFETs, one P-type, one N-type. | [
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And of course, we draw it like that. This is how we actually implement an inverter with two MOSFETs, one P-type, one N-type. Let's do a little more complicated gate. So let's go through and analyze this one. So we'll start with A and B equals 0. So there's A. So what about that top transistor, on or off? Off. Good. Bottom one? Off. Off. Good. OK, let's put B's labels. It's also at 0. | [
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OK, let's put B's labels. It's also at 0. We're going to do the first row of the truth table first. So what's this upper B transistor? On. And the bottom one? Off. Good. OK, so path then goes from Q where? Yeah, up to VDD, right? OK, so we get a 1. Good. Seem to follow that? Seem like it. OK. Feel free to ask questions. So let's see. Here, the A value is the same, right? We're going to look at the 0, 1 row, the second row. | [
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So let's see. Here, the A value is the same, right? We're going to look at the 0, 1 row, the second row. The A value is the same. So it just left the markings on A. You already told me the answer is there. So let's just change B. So B will have 1.5 volts. So what about B's upper transistor? Off. Good. And the bottom one? On | [
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Good. Seem to follow that? Seem like it. OK. Feel free to ask questions. So let's see. Here, the A value is the same, right? We're going to look at the 0, 1 row, the second row. The A value is the same. So it just left the markings on A. You already told me the answer is there. So let's just change B. So B will have 1.5 volts. So what about B's upper transistor? Off. Good. And the bottom one? On. | [
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Good. And the bottom one? On. So now where does Q connect? Down to ground, right? Good. OK, so what's the answer? 0. Good. So now I'm going to skip a row of the truth table because I just want to change one bit. So I'm going to go down to the 1, 1 row. So now B is the same, right? B is still 1. So I've left the B markings there. So now let's put A markings for 1. So 1.5 volts. So top transistor? Off. | [
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5 volts. So top transistor? Off. Bottom left? On. OK, so Q still actually now has two paths down to ground, right? So that'll still be ground. And then let's do that last row. Here again, from the bottom row, A is the same. It's still 1. So I'll leave those markings. And we'll put the B markings for 0 back. So you already solved this, but let's just go through it again. The upper B transistor? On. | [
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So you already solved this, but let's just go through it again. The upper B transistor? On. And the bottom one? Off. Good. OK, so we still have a path down to ground. It's still 0. So what is that? Not put together with OR. Yeah, so not put together with OR, right? OR it together, and then invert the output of the OR. That equation. So that we call a NOR gate. It stands for not OR. And it looks like this. | [
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It stands for not OR. And it looks like this. So you can see it looks like an OR gate with an inverter bubble on the front. Yeah. Yeah. How? Oh, it doesn't matter. It's just two ways to go down to ground. They're just electrically connected. Yeah, the thing you have to worry about, rather, when you design gates, is you want to make sure you never have a path from high voltage down to ground, at least for any long length of time. | [
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They're just electrically connected. Yeah, the thing you have to worry about, rather, when you design gates, is you want to make sure you never have a path from high voltage down to ground, at least for any long length of time. Because if you do that, current will flow very quickly, and your chip will melt. So you need to make sure that you never set up your transistors in a way that it's possible for current to flow directly from high voltage to ground. | [
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Because if you do that, current will flow very quickly, and your chip will melt. So you need to make sure that you never set up your transistors in a way that it's possible for current to flow directly from high voltage to ground. Yeah. But in this case, having two paths to the same voltage, that's OK. It actually will just go down to ground faster. It has less resistance to ground. | [
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It actually will just go down to ground faster. It has less resistance to ground. OK, that's an OR gate. One more. So let's do this a little more easily. So let's just say A equals 0. So I won't even tell you what B is here. So let's just look. What happens if A equals 0? So what's the top transistor going to do? That one's on. The other A transistor? Off. Do I need to look at B? I don't, right? Because I have a path already from Q up to VDD. | [
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The other A transistor? Off. Do I need to look at B? I don't, right? Because I have a path already from Q up to VDD. So any time A is 0, Q is what? A 1, right? Good. Now, what about B equals 0? The same, right? The circuit is symmetric. It has the same behavior for A and B. Let's just walk through it | [
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The other A transistor? Off. Do I need to look at B? I don't, right? Because I have a path already from Q up to VDD. So any time A is 0, Q is what? A 1, right? Good. Now, what about B equals 0? The same, right? The circuit is symmetric. It has the same behavior for A and B. Let's just walk through it. So we'll put 0's in B, top transistor on, bottom one off. There's a path, right? So also, 1, 0 gives us a 1. | [
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So we'll put 0's in B, top transistor on, bottom one off. There's a path, right? So also, 1, 0 gives us a 1. So then we have one last case, which is A and B are both equal to 1. So what about A? What about that top transistor? Off. Bottom? On. And then B, also 1.5 volts. Off and on. Good. So we've got a connection down to ground now. All right? What is this gate? An AND. Good. And it looks like that. | [
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Good. And it looks like that. AND gate with a bubble on the front. So you do the AND, and then you invert the output. I'm sorry? Can you combine it with a NOT gate? Yes, you can combine it with a NOT gate to get an AND gate. So you can take the NAND and put a NOT on front if you want to build an AND. In most of the systems we'll design, actually, you'll see that usually you have more than one level of gate. | [
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So you can take the NAND and put a NOT on front if you want to build an AND. In most of the systems we'll design, actually, you'll see that usually you have more than one level of gate. And so you end up using pure NAND or NOR most of the time, whenever you can. Because otherwise, you're using more transistors than you need to. Yeah, you can make an AND gate by just adding an inverter on the front. | [
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Because otherwise, you're using more transistors than you need to. Yeah, you can make an AND gate by just adding an inverter on the front. OK, so there are some rules. Same number, one side's parallel, at least for NAND and NOR. One side's parallel, the other's serial. I'll explain duals maybe the end of this week or next week. But for now, it's enough to know the parallel versus serial construct. | [
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I'll explain duals maybe the end of this week or next week. But for now, it's enough to know the parallel versus serial construct. So I'm going to switch over to the tool, and then maybe you can help me out. Let's see. Yeah? I think you had a question earlier that I asked. OK. Do you want to ask now, or I can switch back? Good question, but let me come back to that one, actually. Yeah. | [
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Do you want to ask now, or I can switch back? Good question, but let me come back to that one, actually. Yeah. I have to convince my laptop. PowerPoint doesn't like you to look at other things. OK, so now we're going to go down to the CMOS gate layout tool. And you'll see that I actually pre-wrote. Wait for that to go away. So why don't we do the NAND? OK. So there's a NAND gate with two inputs. | [
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So why don't we do the NAND? OK. So there's a NAND gate with two inputs. You can check it by saying, hey, I think this is a NAND gate with two inputs, and pushing check answer. And it'll put it all green, meaning it's correct. You can go click on these rows, and it'll put the values at each of the junctions. But let's extend this and make this three inputs. So actually, here is a three input NAND exercise. | [
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But let's extend this and make this three inputs. So actually, here is a three input NAND exercise. We can check answer. And so at least one of those is wrong. If I have three inputs, well, it's not even paying attention to C. So what do you suggest I do to make this a three input NAND gate? Yeah, so add one p-type and one n-type controlled by C. So where should I put them? You can put the C. | [
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So what do you suggest I do to make this a three input NAND gate? Yeah, so add one p-type and one n-type controlled by C. So where should I put them? You can put the C. Hm. Up here somewhere. So up here somewhere? Right. Hm | [
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So actually, here is a three input NAND exercise. We can check answer. And so at least one of those is wrong. If I have three inputs, well, it's not even paying attention to C. So what do you suggest I do to make this a three input NAND gate? Yeah, so add one p-type and one n-type controlled by C. So where should I put them? You can put the C. Hm. Up here somewhere. So up here somewhere? Right. | [
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Up here somewhere. So up here somewhere? Right. Hm. See this thing turned to S? It means short. This is what you don't want to do. I didn't do what Rahul said yet. This is not his fault. But I connected the top through C. And so now, I actually created a path from high voltage down to ground, in this case here, where I've got 1, 1, 0, and A, B, and C. Yeah. Yeah, because I didn't protect the bottom to connect to ground. | [
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Yeah. Yeah, because I didn't protect the bottom to connect to ground. So now I have to do the other half of what Rahul was saying. And I will snip off this ground, add another n-type down here, connect those up, label that C, connect the other side to ground, and then check answer. So hopefully, you understand this side is in series. If you wanted three, you put three. If you want four, you put four. | [
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If you wanted three, you put three. If you want four, you put four. Four is about where it gets a little too slow. And so typically, gates will scale to about four inputs. And then you'd want to use multiple gates. But you can generalize these if you want to. If you want to play with it, you can go to the tool and make sure you understand it, build whatever you want. You can actually ask the question you asked there, Daniel, also. | [
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If you want to play with it, you can go to the tool and make sure you understand it, build whatever you want. You can actually ask the question you asked there, Daniel, also. Maybe what I'll do is just reload it. It's easier than trying to delete everything. But for example, if you put the n-type on top, then you'll get these things, L and H, which if you look down in the legend here, you'll see stand for soft 0 and soft 1. | [
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It's easier than trying to delete everything. But for example, if you put the n-type on top, then you'll get these things, L and H, which if you look down in the legend here, you'll see stand for soft 0 and soft 1. So if you think about the way these things work, usually people ask this question, so it's good you asked it. But if you think about the way these things work, remember, for example, the n-type up there, the voltage has to exceed a threshold for it to turn on. | [
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] |
So if you think about the way these things work, usually people ask this question, so it's good you asked it. But if you think about the way these things work, remember, for example, the n-type up there, the voltage has to exceed a threshold for it to turn on. And so if A is at high voltage, then it will turn on so long as the other side is not at high voltage. Once it comes within the threshold of high voltage, it will actually turn itself off. | [
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And so if A is at high voltage, then it will turn on so long as the other side is not at high voltage. Once it comes within the threshold of high voltage, it will actually turn itself off. And so the output there, the thing that comes out the other side, is actually a little lower than high voltage. I think I misquoted before. The threshold is usually only about 20% or 30%. And so what comes out here is about 70% or 80%. | [
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The threshold is usually only about 20% or 30%. And so what comes out here is about 70% or 80%. And we call it a soft 1. And that soft 1 will be then slower in pulling up the next gate up to high voltage. And if you keep building things this way, eventually they just won't work, because they won't be able to exceed the threshold voltage. So because of the way MOSFETs work, typically we're not using this kind of approach often directly. | [
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And if you keep building things this way, eventually they just won't work, because they won't be able to exceed the threshold voltage. So because of the way MOSFETs work, typically we're not using this kind of approach often directly. Instead, we build with NAND and NOR. This is how you would build NAND and NOR if you wanted to. But people rarely do this in practice for that reason. | [
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This is how you would build NAND and NOR if you wanted to. But people rarely do this in practice for that reason | [
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And that soft 1 will be then slower in pulling up the next gate up to high voltage. And if you keep building things this way, eventually they just won't work, because they won't be able to exceed the threshold voltage. So because of the way MOSFETs work, typically we're not using this kind of approach often directly. Instead, we build with NAND and NOR. This is how you would build NAND and NOR if you wanted to. | [
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Instead, we build with NAND and NOR. This is how you would build NAND and NOR if you wanted to. But people rarely do this in practice for that reason. Yeah? How many NORs do you want in each? Yes, they're complementary structures. So you've got at least one of each. So there's no gate that has fewer than two. The NOT gate's the simplest. Yeah? OK, yeah, so this was actually a comment also along the lines of your question, Daniel, that if you swap them, you do get these soft 0s and soft 1s. | [
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The NOT gate's the simplest. Yeah? OK, yeah, so this was actually a comment also along the lines of your question, Daniel, that if you swap them, you do get these soft 0s and soft 1s. Coming out, they don't quite work properly. Does that answer your question? OK. All right, so what I want to do next is take a look at a function and think about what we can do to get a nice way to express the function. | [
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Does that answer your question? OK. All right, so what I want to do next is take a look at a function and think about what we can do to get a nice way to express the function. So let's see. Well, kind of hard to understand that probably at this point. So let's start by doing something we know. So when we did the logical completeness proof, we went and we looked at each of the lines with a 1, and we wrote down a Boolean expression for each line. | [
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So let's start by doing something we know. So when we did the logical completeness proof, we went and we looked at each of the lines with a 1, and we wrote down a Boolean expression for each line. And then we ORed them together to get the function. So let's do that. So here's a row. How do I write a function that gives me that row? Yeah, a b complement c. Remember that we've got each of the variables. | [
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How do I write a function that gives me that row? Yeah, a b complement c. Remember that we've got each of the variables. So this one is a 1, so we'll have a. 0 will give us b NOT. And c will give us c. So that'll be a b prime c. So what about this row? a b c prime. Good. What about this row? a b c. Good. So if we take those three and we OR them together, we get f. So it turns out I could also write f is a b plus a c. | [
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So if we take those three and we OR them together, we get f. So it turns out I could also write f is a b plus a c. So you can verify that if you want. The ones where a and b are on are these two down here, the bottom two. And of course, you have ones there. And the ones where a and c are on are the bottom one, and then the sixth one down from the top, or the third from the bottom. And of course, those are both 1 also. | [
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And the ones where a and c are on are the bottom one, and then the sixth one down from the top, or the third from the bottom. And of course, those are both 1 also. And together, those two sets give me all three of the rows with 1. So that's the same function. And if you remember distribution, distributivity, well, this, if I have a times b, then that'll give me that term. a times c, that'll give me that term. | [
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And if you remember distribution, distributivity, well, this, if I have a times b, then that'll give me that term. a times c, that'll give me that term. So all three of those are the same. Which one's the best? Yeah. How did you do that? I just made it up for now. I just said, hey, I just happen to know what this is. I'll show you a way later. Good question, though. Yeah. OK. That's one way to count. | [
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OK. That's one way to count. Good answer. Yeah. I was about to say, yeah. OK. So you also like the third one. Sorry, but we didn't agree on a metric. If we don't agree how to measure things, then all answers are wrong, right? It's the same sort of game you can play with, add the numbers between 1 and 3 or something | [
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