 Hi, I'm Zor. Welcome to a new Zor education. Let's continue talking about implementation of certain aspects of mathematical logic in electronics. The previous lectures were dedicated to implementation of binary logical operations like logical war or disjunction, logical and, or conjunction, and exclusive war, XOR, which is sometimes called addition by modulator. Today we will talk about unary operation, which is negation or inverting, not operation, not. So obviously, not operation has only two different arguments, and the result of the operation is not 0 is 1 and not 1 is 0. Not true is false, not false is true. That's by definition. Okay. Now, this lecture is part of the course. The course is called Physics for Teens. It's presented on Unizor.com, and I suggest you to watch all the lectures from that website, because every lecture has detailed notes with pictures much better than whatever I'm trying to draw here on the board. Well, the site has exercises, exams. There is a prerequisite course called Math for Teens, which is, well, not the course itself, but whatever is presented in the course. The knowledge, mathematical knowledge is mandatory to learn physics. Okay. Yes, and the site is completely free. There are no advertisements, no financial strings. You don't even have to log in. Okay. So, let's talk about implementation of logical not operation in electronics. Let me start with not exactly electronic implementation. Here is what I mean. Consider we have the source of electricity. We have a battery, which has plus and minus. And to the plus, I will connect through some kind of resistor. I will connect my output point output. If nothing happens, if there is nothing else on the schema, the positive potential at this terminal of the battery will be exactly the same as this one. So it's always one. It's always true, always positive. Now, let's continue. What if I will connect to the ground? Well, here is what will happen. Now, this is the positive potential. Ground is neutral. It's an unlimited source of electrons if there is some attracting force which brings them out. So, obviously, this is positive. This is positive. And the electrons will go this way. Well, the current obviously goes opposite way. And there is certain drop of potential. If this is, let's say, whatever, the 5 volt plus 5 volts, and this is 0, then you can actually, based on the resisting properties of this resistor, you can calculate the current. But the potential in this particular case would be the same as this one, as 0. The potential from here will drop to 0 here. And that's what that basically current means. And the current will go this way, electrons will go this way. So in this case, output will always be 0. So if there is no ground, output is always 1. If there is a ground, output is always 0. How can I make it in both ways? Well, very easily. Let me introduce a mechanical switch. So if this switch is in on position, my output will be 0, same as ground. If this switch is off position, my output will be the same as positive terminal of the battery, some kind of a positive. Now, the positive is associated with 1, and 0 is associated with 0. So if switch is in on position, that would be 0. If switch is off position, that will be 1. So let me just write it down. On, 0, off, 1. Now, if I will implement the switch electronically in such a way that on position corresponds to 1 and off position corresponds to 0, then I will have exactly what I need, from 1 to 0, from 0 to 1. That would be an operation of negation. So how can I implement the switch electronically? Well, we actually know what it is. We have learned about triodes, right? So what's the scheme of triode? This is anode, this is cathode, and it's hot, basically. The way how we increase the temperature is irrelevant right now. But basically, yeah, there is some kind of filament here with another battery which heats this element, which heats the cathode. Now, the cathode is connected to something. Now, if cathode is, now, this is what I would just draw. This is the diodes, if you remember, right? So if my cathode has negative potential and heated, and if anode has a positive potential, and then since it's heated, there is an electron cloud here. We have a termionic emission, and the electrons will be attracted to anode, and there will be basically the flow of electrons. If this is minus, this is a plus, there will be always the flow of electrons this way, and current goes this way. Now, what triodes introduce is a grid here. Now, if grid is positive, then it actually accelerates the electrons, because positive grid attracts, right? So it accelerates electrons. Well, some of them probably will hit the grid, but most of them will go through the openings in the grid and will fly to anode. And actually, we will increase the potential, the positive potential of the grid. The speed will be increased as well, so the current will be greater, right? So this is a triode. Now, what if the potential on the grid is negative? Well, if it's negative, it doesn't really allow electrons, it reflects electrons back to the cathode and there is no current. So using this grid potential, we can actually control the flow of electrons. We can increase it by increasing the positivity of the grid, or we can decrease it by going down to zero and maybe even to negative. Now, what if it's zero? Well, then it actually acts like diode in a way. And if the anode is far away, sufficiently far from cathode, then zero potential will actually result in basically no electrons going to anode from the cathode, because even if there are three electrons, but they're not really close enough to anode to be attracted, or if there are some which are attracted, it's very minimal amount. Not exactly the same as if my grid is positively charged. If it's positively charged, electrons are accelerated and they will definitely go in a much greater amount to anode. So basically changing potential from plus to zero changes the flow of electrons from intense when it's plus to almost zero when the grid is at zero potential. So that's exactly what we need right now. We need the switch. If this is on, which means it's positive, the grid, we have the direct connection. So if I will replace this with a triode, if I will put plus here to the grid, there will be a connection. So there will be a connection. The electrons will go and the potential at the output will be exactly the same as potential of the grounding, which is zero. So plus, and plus is always associated with one, will be converted into zero. So this is my input. So if input on the grid is one, which means positive potential, the grid will increase the speed of electrons and electrons will go to anode from cathode. There will be a straight connection and the output will be the same as the ground, which is zero. Because this resistor actually prevents potential to be completely delivered to the output point. So electrons will go this way and then this way. And obviously we can calculate the parameters of a triode and this resistor in such a way that basically we have the same potential here as here in case my input is one. Which means positively charged here. And if the input is at zero, so the grid doesn't really help electrons to move this distance from cathode to anode. And if the distance is significant enough, so very few electrons actually are reaching anode by themselves. You see, if it's just an electron cloud, it's somewhere concentrated around the cathode. And we need some force actually to bring it to anode. Now, what can be this force? Well, maybe we can increase the intensity of the temperature that would increase the speed of the electrons, but they're still chaotically moving. So some of them will reach. That's how diodes are working actually. They're very close. Anode and cathode are close enough and the temperature is probably five. But if temperature is not high enough, so electrons are in the cloud but not too many and not such a big speed of each of them and they're chaotically moving around the cathode. It's the grid actually which picks them up if it's positively charged and accelerates to the anode. And if the grid doesn't do it, then there is practically no movement of electrons from cathode to anode. So in most of these cases, I mean we can definitely talk about characteristics of this resistance and this tryout in such a way that since there is practically no electrons moving here, then there is no current and if there is no current, the potential actually will be exactly the same here and it will be positive. So zero here on the input will result in positive which is one on the output and one on the input which is plus positive will result in connection and it will be zero at the output. That's exactly what we need to implement inverter. So input is a grid and output is this point connected to anode of the tryout. And that's how the operation, logical operation NOT is implemented in electronics. Now again, this is implementation based on vacuum tube tryout. But again, most importantly is the functionality of the tryout that there is something which controls the flow of electrons. The same concept of the tryout can be implemented in semiconductor and transistors and that's just a different implementation of the same functionality. In this case, my most important point was the functionality of the tryout which is basically working like a switch right now. So sometimes it works for like, if you remember, amplifying the signal. The same idea basically. That's it. So the functionality is the most important. All these lectures related to implementation of logical operations, I was actually presenting using the old vacuum tube based construction of the diodes and the tryouts. But it's irrelevant because what we were using, we were using the functionality. And we can definitely implement the same functionality using much better technology, contemporary technology of semiconductor integrated schema, etc. Circuits. Well, that's it. I suggest you to read the notes for this lecture. There are, again, a little bit better pictures than whatever I draw. And what else? Basically, that's it. Thanks. Thanks very much and good luck.