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EEVacademy | Digital Design Series Part 1 - Introduction To Digital Logic

Mar 22, 2024
Hi, I thought I'd try something a little different today. Look at this. The reason you're looking at a blank white screen with a cursor is because I have a new Wacom Intuos tablet and I'm pretty enthralled by this thing. That's one of these pen-based tablets that allows me to draw and, as artists, use these things, you know, do graphic and

digital

art, you know animation and all that kind of stuff, you can use them as simple drawing tablets like this, so I thought I tried to make some tutorial type videos using this capture tablet and I want your feedback on this, whether or not you like this format or not, because I can do some fun things with it.
eevacademy digital design series part 1   introduction to digital logic
I can change colors instantly and it's like I can. I leave a light or dark touch like this and I can change my pen styles. I can instantly press a button and scream if I press the right button, anything elevated and I can do a lot of much more sophisticated artistic things like this, but it's really nice to be able to, you know, do a drawing-based tutorial, like my usual stuff from Dave CAD you're no doubt familiar with so I thought I'd give it a try so I'd really like your opinion on whether you think or not.
eevacademy digital design series part 1   introduction to digital logic

More Interesting Facts About,

eevacademy digital design series part 1 introduction to digital logic...

This is a good idea and I'll probably post a poll somewhere up here in the corner. It should automatically appear whether or not you want to see more of this style of tutorial and whether you would really like to see it or not. this on a second channel, like moving this screenshot type tutorial content to its own dedicated web channel, that's all I uploaded, so let me know if you think it's a good idea or not and let me know what you name it would like. If you like the idea of ​​what name you would like to call on our second channel, it could be like Evie learn or Evie tutorial or Evie University or something like that, please let me know, yes, a unique YouTube survey popup appears and we work anyway.
eevacademy digital design series part 1   introduction to digital logic
It comes to this, so what is

digital

logic

and how does it differ from the analog world? Well, you might be familiar with a sine wave, for example, and that means zero volts here and one volt here and - 1 volt here, for example, and this is it. a representation of an analog signal Anton can vary anywhere you know within that range for example, but you may be familiar that a digital system is represented like this, it just has two

part

icular levels like this and these can be called

logic

1 and logical 0. be called 5 volts and 0 volts, it could be 3.3 volts and 0 volts could be our common voltages, for example, there are others, it simply represents a binary representation of analog voltages, so digital is still analog in terms of the form real wave, but in the way it is interpreted. and it is represented only in binary form like this and it could be called 1 or 0, also called true/false for example, and you know whatever name you want to give it, it doesn't matter, it represents 2 different logical states and because digital still lives. in the analog world then we have to set limits if this is 0 volts here and this is 5 volts here for example our waveform is not going to be absolutely perfect so you know it might be like this but it might not be right 0 and 5 volts, so we have to set limits here where something is determined to be a logic 1 and a logic 0, so in this

part

icular case 4 volts might be safe, just as an example, and anything greater than 4 volts, so anything here is determined to be a logical 1 and likewise anything here is determined to be a logical 1 and anything like this here is determined to be a logical 0, so these levels can be call 1 and 0 true and false high and low where 5 volts and 0 volts whatever you want to call it, but when the signal is within this region here, then it is an undefined state.
eevacademy digital design series part 1   introduction to digital logic
Digital doesn't know what to do with it, the systems don't know what to do with it, so if you have a slow change in signal like this that increases from 0 to 1 volt like this, then this period of time is unknown, so its digital system won't know how to interpret it, that's why it always sees digital signals only 1 or 0 with an edge as fast as humanly possible, so in a typical digital logic system we could have a chip here for example that is connected to ground and is connected to 5 volts or 3.3 volts, for example, are very typical modern digital logic levels. or even less, you know, 1.8 1.2 volts, it doesn't matter, it will represent a binary value 1 and 0 true and false high and low and you will have several inputs to the chip and you will have several outputs to the chip and these will all be 1 or 0 either 1 or 0 i.e. in the case of a 5 volt rail chip you would have 5 volts here and you would have 0 volts here and you expect 5 volts on the input and 0 volts on the input here with those margins of which we talked about before so what we need to do is look at our basic digital gates, all of these chips will contain digital logic or what are called digital logic gates and there are only a handful of different types of gates that can be used to form any chip, Whether it's your latest Intel microprocessor, which has a hundred million gates in the thing or they talk in terms of transistors, you can think of transistors as gates because they're going to turn off. and so on, but we won't go into details there, so let's take a look at your basic logic gates.
Now there are three types of basic doors that you will need to know to get started: the end door, the or door, and the not door. more commonly known as an inverter or inverter gate, so let's look at the traditional symbols for these, there are two different types of symbols, which makes it a little confusing. You should know both now that they're both defined by I. Triple E and IAC and that kind of thing, but I'm going to call them the traditional style, you know, so the traditional style and the door are like this with a curved line like that, you can Think of it as a D, just remember. the D and do like this so that it has one output and at least two inputs, since we will see a logic, a final gate needs at least two inputs, it can have more, but that is a special case now, the o gate actually has this shape, curved there and then, so it's not very good, so we'll draw that one a little better once again, two entrances in one exit, now the door is no different because it only has one entrance and one exit. and it has this circle at the end here and this is the circle that is known as the knot symbol, so the investor symbol, if you just want to draw it alone, is the triangle plus a little knot there, now this knot can be used in it's proprietary and you've probably seen them on data sheets and chips and things like that, the actual symbol on the pin, you know, it may have this little knot on it, it's called this little circle and that implies what that particular pin is. inverted but you also need to know the IEC symbols.
I'll call them and they're all boring square boxes like this and we can put our two inputs into our one output and it has a final symbol in the middle like that, it's actually reasonable. descriptive so from that point of view I don't care at all and occasionally I use them myself and the whole once again our square but it's greater than or equal to one and you'll see why in a minute so again I never liked it a lot that part and now nothing is once again a square, but it has one and then you enter an output, but instead of putting the circle, they define it as a little 45 degree diagonal line like that, so that just implies the knot. function and you may have seen that on some clay chips, it is also now called digital logic for a reason because these gates and/or the inverter perform logic functions that we can use to perform calculations, that is how computers and everything works. the rest.
Meet modern digital, almost everything in modern society works using digital logic. Now we can use what is called a truth table here and you should know them. You must remember them by heart and learn how each particular function works. Now we have two entries. here I've labeled them as a and B and the output C here, so you just draw a table like this with our inputs and now on one side and our output on the other side and basically fill it in with all the possible combinations, so the two inputs could be 0 and 0 low and low could be 0 and 1 could be 1 and 0 and can be 1:1 we have two inputs four possible combinations and you will realize if you know it well, probably not I don't know binary if you are still watching this and this is a binary count of 0 1 2 3 and I have to make a separate video on our binary in number systems and the output is a function of these two inputs here so in this in the an and gate case the output is true or 1 only if a and y get it a and B are 1, then, according to that rule, our am b1 knows that it is not true, es a 0 is both a and B 1 in this case no, it is not a.m.
B 1 in this case no, they are not both a.m. B 1 in this case yes bingo and that is our truth table for gate N, the output here C is only true if inputs a and B are true, that's it and just like the name of the gate and it was descriptive of its functionality here or it's also descriptive of functionality so we write down the four possible combinations, they don't have to be in this order strictly speaking, but by convention they start at zero zero and count up and depending on how many entries you have, let's take a look at this now. the functionality of an o gate is that the output is true, that is, the output is a C is one if I o get it I or B is one, then it is a or B 1 in this case no, both are zero, for so our output is zero. whether A or B one, yes, there is a one, so our output will be one, it is a or b, one, yes, it is and in the final case here they are both one, but that's okay because it is a complete function, it is this one or this one I want yes, so the output is one that is all gate and now the inverter is incredibly easy, we only have one input a and we have one output B, we only have two combinations of inputs high or low, true or false 1 or 0 and our output, the name once again describes the invert function, so inverts basically the inverting polarity is not the correct term, but it inverts the function of the input, so if it is 0 at the input, you get a 1 at the output to 1 at the input gets a 0 at the output, that's simple, that's our inverter now, as far as two front doors coming in and going in or not being the only ones, there's another snowflake special one that I'll talk to you about in a second, but the reason I mentioned these three The first is because with the inverter gates and ands or you can create any other gate, combination or digital system, these three are the ones you need to do all that , actually strictly speaking, that's not true, you just need not and or or the. no and in the end you can create any other possible logic gate or logic system, so we're going to look at a kind of special snowflake here called XOR or exclusive or that's what the X means exclusive because well, it's very exclusive. gate, but you also know a common gate used, so it should form a group along with the other two-gateway types, like this and or and XOR three other main two-gateway types, so let's take a look at the functionality a once again. a b c c z is 1 2 3 dumi sorry, I shouldn't subject you to singing we have our inputs like before oh sorry, I forgot that it's not just a blank box like that, it's actually equal to 1 like that, that's our symbol or exclusive of ICC, so the everyone exclusive function is almost identical to the everyone function here, but it is exclusive, which means that now it has a special functionality like the gate or if I or B is 1, then the output is 1 but with the exclusive case and I guess Can you know that we have a different description for this but the exclusive case that only when I or B is 1 is the output 1 so in this case it is a or b1 not so we get a 0 is a or b1 yes we get a 1 is a or b1 yes we get a 1 is an all b1 in this case for the gate o would have been high but in this case it will give us a 0 so this exclusive o is actually a very powerful function that allows us to make a controlled investment that I could explain later, but still there are three types of two entry gates and/or XOR with the knot.
Now what we can do now is combine the not or inversion function without three other two input doors to give us an agreement. I voted to import gates and these are called NAND gate, nor gate and on the output like that one I showed you before, so it's actually equivalent to getting a physical gate like this and sticking an inverter on the output like that, in fact, you can do that, you can get a physical NAND gate chip, you can get a physical inverter chip. and you can put them like this and it's exactly the same as buying a NAND gate chip like that because that's all it contains inside the chip, it has an additional inverter, not a circuit at the output, now you might think, hey, do we have to Learn more? truth tables for these gates up here and NAND ni and X nothing good, yes, but if you have learned the truth tables or you can derive the truth tablefor and or and All of our imports stay the same, they haven't changed, but in this case we would have a 1 1 1. and a 0, so that's for our NAND function, so that's all you have to do the same way here 1 0 0 0 and 1 0 0 1 for , so let's take, for example, the view, let's take, for example, the NAND gate here like this, okay, we have we have a B and C is our output.
Now I'm going to draw some signs here and it's going to make them completely random and we'll see what we actually get, so if I do this, I don't know how to do it. there's a little growly pulse like that and okay, we have a signal like that and let's do B. I don't know, I haven't really thought about this at all, let's see how it works, so let's look at these two waveforms and see what we get in our C output here using our truth table for the NAND gate, we start off okay, this is a K is 0 and 1, okay, 0 and 1 and 0 and 1, so let's take a look, they're both low, remember? the outputs will only be high when they are both high, so they will be low like this and in this case, well, we can make some dashes down there like this to indicate the time, so let's make the time for each one. transition like this and we can go down and cross and do it now we are following time here so this input is 1 this input is 0 so according to the truth table we will still stay at 0 it's just when let's get to this point.
Here, where both are 1, bingo, this will actually transition to a 1 like this and we'll stay at 1 up to this point. Here where the input goes down, therefore the output must go down with it and we won't do that. You will see a high level again until you guessed it here, but it will only stay because if you follow it down, only a very short period where they are both high will go up, but in this case it will have gone down, so it will stay low. Oops, it's going to go up again because they're both high, look at that and it's going to stay low and low and low until this point here where it goes up and down again, so that's a timing diagram and you can see the relationships. now, if you were to actually physically plug this gate into your board and feed it to digital n C like this, with this time you would get that waveform at the output, you would get a you know, your five volts or 3.3 volts here and your zero volts.
They're too easy, so you might have a ridiculously complicated logic circuit with hundreds or thousands of these gates. Everything will follow these basic truth tables. You haven't learned anything else and there is no more magic in that. That's all there is to analyze in digital. circuits and likewise, if we had a NAND gate there instead of an and gate, we have a simple NAND gate, you guessed it would be the inverse of that because it's not on the output, everything is totally, look now, a little bit, how are you there? go totally inverted, you get the idea, now we move on and I hope you don't lose people here, we move on to what is called boolean algebra, yes, algebra, but in a form of boolean digital logic, now, in this case, the output does not it would be called well, it's still called see, it's labeled see here, but we put what's called a bar on top to indicate that it's inverted, so we would say it's not C output or inverted C output and these things will relate to algebra boolean.
Come on, what? What we've been looking at here is what's called Boolean logic. Booleans are named after George Boole back in the 19th century. He came up with the idea that you know you can describe a system that is 1 or 0 high or low, true or false, and that is So this is Boolean logic, but now we're going to look at Boolean algebra and learn how we can express all of this kind of thing, you know, practically in tables, we can actually express this mathematically and believe me, it's not difficult, stay with me, so we just have mathematical operators that you're familiar with + - you know, multiply, divide, that kind of things.
We also have Boolean operators that describe the mathematics of Boolean logic, so let's take the case of a simple NAND gate, sorry, and a gate here like this, okay, input. an input B there and our output, our output we labeled C before, but let's do this mathematically so that the output is a and and it's represented here is the operator for and as a dot, so I end up B like this and that's it. is the boolean algebra expression for the and gate, so I'm going to draw that back here a and B like this and let's plug the output of this and the gate into the input of an or gate, so we're going to draw our or gate here and let's call this input C because this input here is a and B is the output of that y gate and this is just an input that will call C now, how do we mathematically describe this output here?
Well, we could call this output DS, for example. I called it so D is equal to a and B or the operator the boolean algebra operator for the gate o is a plus C that's it, that's our boolean algebra expression that describes this gate, so you don't actually have to draw these gates if you just said D is equal to a and B or C, so that describes the functionality of that circuit. It's very simple now, just like in regular arithmetic that you are used to, there is an order of operations, for example, you might get confused if this is actually a and B or C or is it a and B or C?
In case you wanted to be really clear, you could put parentheses around a and B to show that, but in Boolean algebra it is assumed that a and the and function will be done first unless otherwise stated, so you could do it if really Put I, if we put parentheses like this, that would imply that we actually had a complete function like this and we had B and C and that was going towards a final function, but with an entry here like this if you draw the parentheses. so you know that the order of the operators matters, so if you want to be really clear then put the parentheses in now, let's not forget the knot symbol, let's say we add an inverter at the input here like this, how would you describe that? well the inverter as I said before uses the bar approach so we will place a bar on top of C and that means it is inverted that is all there is to do and in the same way if we put a knot here at the output of our entire function, so D would then put a bar across the entire expression like this, beautiful, that shows that we have an inverter at the output.
Great, so our logical operators that you see at the end are a dot and or is a plus and the knot is a slash on top of something, so it's going to be a and B a or b and just not a or it could be a plus bi or B and not that, but we we are forgetting about the door , but because it's a special snowflake and we need to mean the symbol logic like this, a combinatorial logic circuit, in this case we have three inputs to B C and we have our output here, we'll call it X, for example.
Now I said before that you can have more than two inputs on any of them, any of your two input gates, your NAND, nor your X or your names and or exclusive or all that kind of stuff, you can have more than one, in this case I have three inputs and one gate, it's called that, although you may not have seen the truth table for this, you can derive it because you would have an extra entry here in this table so you know you would go 0 0 0 0 and then you start 1 0 0 0 1 0 0 1 for example and above, what am I doing there?
We go 1 and 1 like this, so just count for a 3-input gate and do the functions at the output, but again, if each and every input is 1, this input and this input and this input are 1, then the output is 1, so let's try to solve it. what will be our output expression based on this input, so let's take a look here, this is a and this is B, so this is a and B, okay, so this is just as basic with two inputs and gates, now the output here it's a little. The hardest thing we have is that we don't have something like this and B and C, so we have these two Boolean algebra expressions.
Now we can figure out what X is, so this would be a gate or, well, it would be that function with a big knot over the Also, it's beauty, so that's basic digital logic and I'll leave it there because this is enough and we'll need to expand this topic to the simplification of logic boolean and how you can actually simplify your circuits using de Morgan's theorem and Carnot Maps and other techniques to simplify logic because you know if you have a hundred different gates here, if you can get away with it, you know minimize that to fifty gates, so you're going to save the amount of chips that I'm going to say silicon space, you're going to save all that kind of jazz, but I hope you learned a basic

introduction

to digital logic there and it's not that difficult at all once you know the types of Basic logic gates, not many of them learn. how to derive tables aren't hard to memorize either because it's in the name or and you know, it's unique or it's probably the special little snowflake in there, but these things aren't hard at all, so anyway I hope you found them. enjoyed.
If you did, give it a big thumbs up and since this is the first video of its kind, let me know what you think in the comments below or in the e V Log form and if you want to see more of This content is possibly in a second channel. If you think it's a good idea, let me know anyway. I hope you found it useful. See you next time.

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