context
stringlengths 22
3.07k
| embeddings
sequence |
|---|---|
And so scanf will fail, and it will return minus one. If you type something like 42 space hello, it will convert the 42, and then again, it will fail trying to convert hello to the second number. And in that case, having converted one number, it will return the value one. So if you want to check that the user typed the right thing, you can simply compare, and we haven't talked about this if statement yet, but this is something we'll talk about hopefully before the end of the day. | [
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And in that case, having converted one number, it will return the value one. So if you want to check that the user typed the right thing, you can simply compare, and we haven't talked about this if statement yet, but this is something we'll talk about hopefully before the end of the day. If scanf does not evaluate to the number two, so if two is not the answer returned by scanf, then something went wrong. | [
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So if you want to check that the user typed the right thing, you can simply compare, and we haven't talked about this if statement yet, but this is something we'll talk about hopefully before the end of the day. If scanf does not evaluate to the number two, so if two is not the answer returned by scanf, then something went wrong. So scanf should return the number of format specifiers that you asked for. | [
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If scanf does not evaluate to the number two, so if two is not the answer returned by scanf, then something went wrong. So scanf should return the number of format specifiers that you asked for. If it returns something else, the human did something wrong. There are more graceful ways to help the human fix that, but the easy way for our purposes for 120 is to say, well, if they do something wrong, end the program. | [
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If it returns something else, the human did something wrong. There are more graceful ways to help the human fix that, but the easy way for our purposes for 120 is to say, well, if they do something wrong, end the program. Tell them to run it again. So most of the code you'll see will be this simple in terms of how we handle errors. Does that answer your question? All right. OK, so I want to try to cover statements, and then on Friday, we'll look at code examples. | [
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Does that answer your question? All right. OK, so I want to try to cover statements, and then on Friday, we'll look at code examples. So I'll mention I do have handouts. Feel free to take one if you want to look at the code in advance. It's on the links page, too, if you'd rather look at it just online. I do want you to have a handout in class on Friday. So if you take one, please bring it back so that we have enough. | [
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I do want you to have a handout in class on Friday. So if you take one, please bring it back so that we have enough. I think there should be enough, as long as people aren't taking two or three or something. And it is online, too | [
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So I'll mention I do have handouts. Feel free to take one if you want to look at the code in advance. It's on the links page, too, if you'd rather look at it just online. I do want you to have a handout in class on Friday. So if you take one, please bring it back so that we have enough. I think there should be enough, as long as people aren't taking two or three or something. And it is online, too. | [
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I think there should be enough, as long as people aren't taking two or three or something. And it is online, too. And the codes are online if you want to compile them, so you can play with them as much as you want. So remember, I said last week, a statement tells a computer what to do. So let's look at the kinds of statements. We've got three kinds in C. So a statement can actually consist of other statements, which can consist of other statements. | [
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We've got three kinds in C. So a statement can actually consist of other statements, which can consist of other statements. So a big C program will have many very deep, recursively nested statements. But for the little ones we'll look at, they'll be fairly simple. So the three types of statements, you have what's called a null statement, which does nothing. So it's just a semicolon all by itself. | [
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So the three types of statements, you have what's called a null statement, which does nothing. So it's just a semicolon all by itself. A simple statement, I'll show you some more kinds in a few slides. But one kind is just use an expression, follow it with a semicolon. So for example, A equals B. It's an expression. But I want to do an assignment, put a semicolon after it that says, OK, my statement is done. | [
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It's an expression. But I want to do an assignment, put a semicolon after it that says, OK, my statement is done. Go do the assignment for me. Printf, it's a function call. It's also an expression. So expression followed by a semicolon makes a statement, simple statement. You need to have a semicolon. I think someone asked on last week, what if I leave the semicolon out, the compiler will complain. | [
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You need to have a semicolon. I think someone asked on last week, what if I leave the semicolon out, the compiler will complain. Compiler will say, I can't compile this for you. All right, and the third type of statement is a compound statement. And this is a sequence of statements. So you might think, oh, that looks a lot like my main function. In fact, it is. The body of main is simply a compound statement. | [
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In fact, it is. The body of main is simply a compound statement. So you have a list of statements, a sequence of statements that execute in order. So you can put whatever you want. So here I said, OK, radius will be 42. My variable c, which is maybe circumference, I'll calculate as the 2 times pi times the radius. And then I'll print that out. Inside a compound statement, you can actually have additional variable declarations. | [
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And then I'll print that out. Inside a compound statement, you can actually have additional variable declarations. If you want to, you'd put those above the statements. So you can have variable declarations at the start and then statements inside. But we won't use that often in our class. So didn't want to put too much detail. So how do these execute? So there are three things to think about. | [
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So didn't want to put too much detail. So how do these execute? So there are three things to think about. One is a sequential execution. So the function body of main is a compound statement. And they execute in order. So if you have three statements, the first one executes first in the order of appearance in the file. The second one executes second. And the third one executes third. | [
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The second one executes second. And the third one executes third. And when the program is started, all the program does is execute the statements in main in order, in the order they appear. And then the program is done. So here's another one. You actually saw this one already. But I want to make sure you understand it. So you can also introduce what's called conditional execution. So this illustration is a flow chart. | [
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So you can also introduce what's called conditional execution. So this illustration is a flow chart. The way it works is you're going to execute the statement | [
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The second one executes second. And the third one executes third. And when the program is started, all the program does is execute the statements in main in order, in the order they appear. And then the program is done. So here's another one. You actually saw this one already. But I want to make sure you understand it. So you can also introduce what's called conditional execution. So this illustration is a flow chart. | [
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So you can also introduce what's called conditional execution. So this illustration is a flow chart. The way it works is you're going to execute the statement. The first thing you do is you evaluate an expression. So there's some expression you evaluate. And that will either be true or false. Remember, true is anything that isn't 0. False is 0. If it's true, you'll have what's called a then statement, which is a block of code corresponding to when this expression is true. | [
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False is 0. If it's true, you'll have what's called a then statement, which is a block of code corresponding to when this expression is true. And you'll execute that statement. If the expression evaluates to 0, it will instead execute what's called the else statement. So I'll show you how this looks in C. But basically, it's just a choice. Do you do the then or do the else? So here's how it looks in C. | [
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But basically, it's just a choice. Do you do the then or do the else? So here's how it looks in C. So you use what's called an if statement. You put if. You put the expression you want to evaluate here. And then if that expression is not 0, the code that you execute will be between these braces. And you put the else keyword. And you put another pair of braces. And if the expression is false, then this code down here will execute. | [
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] |
And you put another pair of braces. And if the expression is false, then this code down here will execute. You can put any expression you want. And you can also leave off this else if you'd like to. So you can't leave off the first block, but you can leave off the second block and the else keyword. So how do you do that? That's a comment. That's a comment. Yeah. So how do you know that? So that's just how the C language is defined. | [
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Yeah. So how do you know that? So that's just how the C language is defined. So the C language is defined to follow what we call this. This is called a flow chart. So what the C compiler does is it translates this piece of C code into instructions that execute this flow. So it says, OK, first calculate the value of the expression. And if the value is 0, go down to the else statement. | [
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] |
So it says, OK, first calculate the value of the expression. And if the value is 0, go down to the else statement. If the value is non-zero, go to the then statement. And so those statements are arbitrary code. They're compound statements. So you can put whatever code you want there. Does that make sense? Yeah. So you don't always have to put the else. You can say if expression, do something. | [
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So you don't always have to put the else. You can say if expression, do something. And if the expression is false, don't do it. Don't do anything. Just fall out of the bottom and keep going with the next statement. So here's an example. So I could say, well, I want to calculate the inverse of a number. But if that number is 0, I don't want to divide by 0. So first I'll check. Well, is my number not 0? And if it is, I will say inverse equals 1 divided by number. | [
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So first I'll check. Well, is my number not 0? And if it is, I will say inverse equals 1 divided by number. Otherwise, I'm going to print an error message. So that's what this little if statement will do. The test is up at the top here. 0 is not number. If that's true, in other words, number is not equal to 0, then I calculate inverse. Otherwise, I say, oh, something went wrong. Yeah. | [
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Otherwise, I say, oh, something went wrong. Yeah. Well. Is that part of the question? It doesn't really matter. If they're ints, it's not terribly interesting | [
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Otherwise, I'm going to print an error message. So that's what this little if statement will do. The test is up at the top here. 0 is not number. If that's true, in other words, number is not equal to 0, then I calculate inverse. Otherwise, I say, oh, something went wrong. Yeah. Well. Is that part of the question? It doesn't really matter. If they're ints, it's not terribly interesting. | [
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Is that part of the question? It doesn't really matter. If they're ints, it's not terribly interesting. Yeah, so if they're ints, this will generally come out with inverse equal to 0, right? So if they're floats, they wouldn't cause divide by 0. But you would get an infinity, which maybe is also not what you want. So you can maybe think of them as floats. Yeah. Yeah, so the thought was to set the variable value and then to use it later. | [
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Yeah. Yeah, so the thought was to set the variable value and then to use it later. So we'd also, I mean, I'm showing this one statement in isolation. You'd have inverse equal to something else later. You could add the printf inside, as you said. So there are lots of things you could do with it. I just wanted to show you how we use if. Good question. Yeah. Yes. Yeah, so this is a style thing. | [
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Yes. Yeah, so this is a style thing. So any time you have a compound statement, you should increase your level of indentation by whatever your standard is. I usually use 4. A lot of people use 4. Some people use 2, 2 spaces. Some people use 8. And it doesn't really matter what you pick, but everyone on whatever team is working on a program should use the same style. The compiler will not give you an error, but we will mark off points. | [
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And it doesn't really matter what you pick, but everyone on whatever team is working on a program should use the same style. The compiler will not give you an error, but we will mark off points. It makes it really hard to read your code. It makes it very difficult. There are actually tools that will automatically indent it for you. So if you're worrying about it, you can run it through an auto-indent tool. | [
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There are actually tools that will automatically indent it for you. So if you're worrying about it, you can run it through an auto-indent tool. But they'll also do things like decide whether to put braces on or things like that, rewrite your C code for you to make it look nice. OK, any other questions? All right, so here's another example. So let's say I've got a variable size. This is an integer, let's say. | [
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So let's say I've got a variable size. This is an integer, let's say. And I want to make sure size is not bigger than 42. So here I don't have an else. If 42 is less than size, I'm going to change size, and I'm going to tell the user, hey, I changed size. So I'll print out size set to 42, and I'll assign 42 to size. If size was already less than 42 or equal to 42, I don't need to make any change. | [
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So I'll print out size set to 42, and I'll assign 42 to size. If size was already less than 42 or equal to 42, I don't need to make any change. Another way we could use an if statement. Yeah, so in this case, there is no else block. So if this condition is false, it simply comes down to whatever is the next statement after the if. I wanted to give you an example with and without an else. | [
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So if this condition is false, it simply comes down to whatever is the next statement after the if. I wanted to give you an example with and without an else. OK, then the last statement I want to look at is this iterative statement. So if I want to do something more than once, and the number of times doesn't have to be defined. The way I'll decide to stop is I'll have an expression. | [
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So if I want to do something more than once, and the number of times doesn't have to be defined. The way I'll decide to stop is I'll have an expression. So if I want to do something more than once, I can have this structure here. So first I'll have an initialization expression. Then I'll have a test expression. The computer will produce instructions that evaluate the test expression. | [
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] |
Then I'll have a test expression. The computer will produce instructions that evaluate the test expression. And if it's false, I'm done | [
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So if I want to do something more than once, and the number of times doesn't have to be defined. The way I'll decide to stop is I'll have an expression. So if I want to do something more than once, I can have this structure here. So first I'll have an initialization expression. Then I'll have a test expression. The computer will produce instructions that evaluate the test expression. | [
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Then I'll have a test expression. The computer will produce instructions that evaluate the test expression. And if it's false, I'm done. If it's true, I'll evaluate what's called the loop body, then execute an update expression, and then go back up and do the test again. So I'll go around this loop as many times as is necessary until this test expression becomes false. Now, that can be infinite. | [
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So I'll go around this loop as many times as is necessary until this test expression becomes false. Now, that can be infinite. So if you write a loop badly, it just will never finish. Sometimes that's what you want. You might want a program that never stops. So for example, you probably don't want your operating system to say, you know what? My loop finished, and I'm just going to do nothing now. | [
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You might want a program that never stops. So for example, you probably don't want your operating system to say, you know what? My loop finished, and I'm just going to do nothing now. I'm moving on. So an operating system or an online service or something, you would have an infinite loop as the main construct. Just say, OK, keep paying attention to people and doing what they ask. So you can do that easily with a loop. | [
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Just say, OK, keep paying attention to people and doing what they ask. So you can do that easily with a loop. You just make sure the test expression never becomes false. Here's what it looks like in C. We're only teaching you one, but I'll show you another one. So this is the for loop. So you've got your initialization on the left. So you have four open parentheses, initialization expression, semicolon, test expression, semicolon, update expression, close parentheses, and then a compound statement for your loop body. | [
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0.011709487996995449,
0.014994688332080841,
-0.015403633937239647
] |
So you've got your initialization on the left. So you have four open parentheses, initialization expression, semicolon, test expression, semicolon, update expression, close parentheses, and then a compound statement for your loop body. So just to make sure you understand how the flowchart works, I wrote it out as just a list. So what happens is first, the computer evaluates init. After it evaluates init, it evaluates the test expression. | [
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So what happens is first, the computer evaluates init. After it evaluates init, it evaluates the test expression. And if that test expression evaluates to 0, then it's done. It skips to the end of this list, and it moves on to the next statement. Otherwise, if the test is non-zero, that means true, then it evaluates the loop body. It executes the loop body. It's a compound statement, so it'll do a bunch of statements if you put a bunch of statements in there. | [
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] |
It executes the loop body. It's a compound statement, so it'll do a bunch of statements if you put a bunch of statements in there. Then it will evaluate the update expression after it finishes the loop body. And then it will go back to step 2 and evaluate test again. And go around 2, 3, 4, 2, 3, 4, 2, 3, 4 until test evaluates to false. All right, here's an example. So if I want to print the multiples of 42 from 1 to 1,000, I'll start by setting n equal to 1. | [
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All right, here's an example. So if I want to print the multiples of 42 from 1 to 1,000, I'll start by setting n equal to 1. Then I'll check that n has not gotten bigger than 1,000, because I only want to go up to 1,000. My update, you'll notice, increments n by 1. So inside this loop, the first time we execute this loop body, n will be 1. And we'll continue to execute this loop body 1,000 times until n is 1,001, at which point this test will be false and we'll finish. | [
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] |
So inside this loop, the first time we execute this loop body, n will be 1. And we'll continue to execute this loop body 1,000 times until n is 1,001, at which point this test will be false and we'll finish. So for every value of n from 1 to 1,000, we'll check is n mod 42 equal to 0. That would mean n is a multiple of 42. So if it's true, we print that number n using %d followed by a character term. | [
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] |
That would mean n is a multiple of 42. So if it's true, we print that number n using %d followed by a character term | [
0.004222620744258165,
0.003968078177422285,
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] |
And we'll continue to execute this loop body 1,000 times until n is 1,001, at which point this test will be false and we'll finish. So for every value of n from 1 to 1,000, we'll check is n mod 42 equal to 0. That would mean n is a multiple of 42. So if it's true, we print that number n using %d followed by a character term. So this loop will print all the multiples of 42 from 1 to 1,000. | [
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] |
So if it's true, we print that number n using %d followed by a character term. So this loop will print all the multiples of 42 from 1 to 1,000. Very important set of numbers. Yeah? AUDIENCE MEMBER 2. Do you need to define the number of multiples of 42 for a given test? Yes, but that's beyond the scope of stuff I want to talk about. Yeah, yeah, let me not. Ask me afterwards, and I'll tell you why. | [
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Yeah, yeah, let me not. Ask me afterwards, and I'll tell you why. OK, so one more loop. We're actually going to do this loop in class on Friday. So a while loop, basically it's the same thing, but we don't specify the init or the update. So we don't want you to have to learn this in EC 120, but you might see it. | [
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We're going to pick up where we left off. We just introduced Boolean functions. So we're going to look at that, go through, make sure you understand them all, do truth tables for them, and then talk about logical completeness. I think we'll get pretty far through fixed and floating-point. Not sure we'll finish that all today. On Wednesday, we'll wrap up representations, and then on Friday, we'll start talking about C programming. | [
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Not sure we'll finish that all today. On Wednesday, we'll wrap up representations, and then on Friday, we'll start talking about C programming. So that's kind of the look ahead for the week. You have a lab due Wednesday, shortly after class. So if you haven't looked already, please look soon. I decided because one of my colleagues told me that some of our students, particularly freshmen, kind of got panicky a little bit last year, or last semester rather, and so I will go hang out in the lab tomorrow for office hours. | [
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So if you haven't looked already, please look soon. I decided because one of my colleagues told me that some of our students, particularly freshmen, kind of got panicky a little bit last year, or last semester rather, and so I will go hang out in the lab tomorrow for office hours. So I know a couple of you asked me, and normally I'm at Mia Zaw's on Green Street, but instead I'll go sit in the lab. | [
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I decided because one of my colleagues told me that some of our students, particularly freshmen, kind of got panicky a little bit last year, or last semester rather, and so I will go hang out in the lab tomorrow for office hours. So I know a couple of you asked me, and normally I'm at Mia Zaw's on Green Street, but instead I'll go sit in the lab. So, you know, if you were thinking of coming to office hours, it would be a good chance to do the lab. | [
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So I know a couple of you asked me, and normally I'm at Mia Zaw's on Green Street, but instead I'll go sit in the lab. So, you know, if you were thinking of coming to office hours, it would be a good chance to do the lab. It's like 12 pages of reading. So, you know, it's a lot of reading. It's not actually that much work, I think. How many of you have done it already? Just out of curiosity. | [
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It's not actually that much work, I think. How many of you have done it already? Just out of curiosity. Oh, awesome. Good, good, great. So, you know, if you're one of the people in the room and there's feeling like, wow, I haven't done this and I'm feeling panicky, hopefully you can make it tomorrow to my office hours, sit down, do it, and I can help you out if you're having problems. | [
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Good, good, great. So, you know, if you're one of the people in the room and there's feeling like, wow, I haven't done this and I'm feeling panicky, hopefully you can make it tomorrow to my office hours, sit down, do it, and I can help you out if you're having problems. Otherwise, there are lots of office hours. So look on the schedule on the wiki, and you can find other people. Okay, so a couple reviews. | [
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So look on the schedule on the wiki, and you can find other people. Okay, so a couple reviews. So we talked about four functions on Friday. We talked about the AND, which is the all function. So if all of the inputs are 1, it outputs a 1, otherwise a 0. We talked about OR. If any input is 1, it outputs a 1, otherwise outputs a 0. We talked about NOT, which is just complement. Put in a 1, get out a 0, put in a 0, get out a 1. | [
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We talked about NOT, which is just complement. Put in a 1, get out a 0, put in a 0, get out a 1. And we talked about XOR, exclusive OR, and how it expands, which is the ODD function. So if an odd number of inputs are 1, it outputs a 1, otherwise outputs a 0. So those are the four we looked at. And I introduced this idea of a truth table. So again, a truth table is just a way of writing down a Boolean function. | [
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And I introduced this idea of a truth table. So again, a truth table is just a way of writing down a Boolean function. So we write down the inputs on the left side of the line. We write all the combinations, usually in binary order, given the order we've listed the variables. And then on the right side, we can put the outputs for each of those lines. Okay. So last time I kind of bungled my my management of my display. | [
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Okay. So last time I kind of bungled my my management of my display. So this time, let me just go show you. So again, this is the easiest way I know to find things. It happens to involve going through my website. But there on the F16 link, you can find all of these exercises. And down here, there's lecture videos and lecture slides and stuff like that. But just to remind you, there's these tools here. | [
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And down here, there's lecture videos and lecture slides and stuff like that. But just to remind you, there's these tools here | [
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Okay. So last time I kind of bungled my my management of my display. So this time, let me just go show you. So again, this is the easiest way I know to find things. It happens to involve going through my website. But there on the F16 link, you can find all of these exercises. And down here, there's lecture videos and lecture slides and stuff like that. But just to remind you, there's these tools here. | [
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And down here, there's lecture videos and lecture slides and stuff like that. But just to remind you, there's these tools here. And so if you want to practice practice unsigned or practice twos complement, you can change the number of bits. If you really want to challenge, you can go to 16. I don't think there's really that much practical utility in doing that kind of long example. But if you really want to make sure that you can do that repetitive translation stuff, you can play with 16 bits or you can do it with as few as four. | [
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I don't think there's really that much practical utility in doing that kind of long example. But if you really want to make sure that you can do that repetitive translation stuff, you can play with 16 bits or you can do it with as few as four. You can see at the top, there's also a floating point. So when we talk about that today, you can play with that. There's also bits, which are the four functions that I told you about just a second ago, the Boolean functions. | [
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So when we talk about that today, you can play with that. There's also bits, which are the four functions that I told you about just a second ago, the Boolean functions. And you can make sure you understand applying those to sets of bits. You can also go do things like extend. So if you want to sign extend, twos complement pattern, make sure, you know, just copy the sign bit, right? So it's basically just copying. | [
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You can also go do things like extend. So if you want to sign extend, twos complement pattern, make sure, you know, just copy the sign bit, right? So it's basically just copying. But just to make sure that you understand all the material, there's a lot of different exercises in here. If you feel uncomfortable with anything, it'll give you instant feedback. Let's see if I can get this one right. | [
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If you feel uncomfortable with anything, it'll give you instant feedback. Let's see if I can get this one right. Kind of embarrassing, wasn't it? Oops. Okay, looks like I got it all right. So if on your mobile, you can push the button on your, if you're typing on your laptop, you can push the button with the mouse or you can push enter. It'll highlight the ones you got right in green. | [
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So if on your mobile, you can push the button on your, if you're typing on your laptop, you can push the button with the mouse or you can push enter. It'll highlight the ones you got right in green. If you put something wrong, again, it'll show you what you got wrong. So let's just go put a couple wrong. So those will show up in gray and you can go back and check them. So you can do as many exercises you want. | [
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So those will show up in gray and you can go back and check them. So you can do as many exercises you want. Just make sure you understand how things work. So let me switch back to PowerPoint. All righty. So those are the exercise tools. All right. So now let's go through our four functions and I want you to help me kind of fill in these truth tables. So let's start with and. And I'll also give you some more notational knowledge and how to draw gates and stuff like that. | [
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So let's start with and. And I'll also give you some more notational knowledge and how to draw gates and stuff like that. So let's start with and. So what's zero and zero? Good. What's zero and one? Good. One and zero? Good. One and one? Good. So with two inputs, they all have to be one, meaning both of them have to be one. All right. So this is the and function. We don't usually write it out with words, right? We'd like to be a little more concise with our Boolean expressions. | [
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So this is the and function. We don't usually write it out with words, right? We'd like to be a little more concise with our Boolean expressions. So usually we'll use this multiplication notation from normal algebra. Okay, so if I write something A times B, it means A and B. Okay, there are other notations people use in mathematics. It's called a conjunction. So if you end up taking a math logic course or something, you'll see that notation. | [
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It's called a conjunction. So if you end up taking a math logic course or something, you'll see that notation. We also use gate diagrams. So this is an and gate here. There are two features that distinguish it from other types of gates | [
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So usually we'll use this multiplication notation from normal algebra. Okay, so if I write something A times B, it means A and B. Okay, there are other notations people use in mathematics. It's called a conjunction. So if you end up taking a math logic course or something, you'll see that notation. We also use gate diagrams. So this is an and gate here. There are two features that distinguish it from other types of gates. | [
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So this is an and gate here. There are two features that distinguish it from other types of gates. So when you start drawing gates, if you're drawing them by hand, make sure that you try to get a flat input and a rounded output and then people will know you mean an and gate. Okay, so that's that's and. So what about or? Let's go through and do the truth table first. So remember or is the any function. | [
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So what about or? Let's go through and do the truth table first. So remember or is the any function. So zero or zero? Good. Zero or one? One or zero? One or one? Good. Okay, so you guys know these pretty well, it seems. So we also use algebraic notation. So for or we use plus. Okay, so multiplication is and, addition is or when we write Boolean expressions. Again, math terminology or math notation, it's called a disjunction. | [
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Okay, so multiplication is and, addition is or when we write Boolean expressions. Again, math terminology or math notation, it's called a disjunction. It's written with that little B there. And or gate, again, two distinguishing features, rounded input, pointy output. Okay, so if you draw things, just make sure that you get those two sides right and then people will be able to tell what it is. | [
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And or gate, again, two distinguishing features, rounded input, pointy output. Okay, so if you draw things, just make sure that you get those two sides right and then people will be able to tell what it is. If you scribble it so quickly that we can't tell if the back of the input side is round or straight and you scribble the front side so we can't tell if it's pointy or round, then we won't know what it is. | [
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Okay, so if you draw things, just make sure that you get those two sides right and then people will be able to tell what it is. If you scribble it so quickly that we can't tell if the back of the input side is round or straight and you scribble the front side so we can't tell if it's pointy or round, then we won't know what it is. Just do it carefully enough that you can tell those two things and then people can tell what you're trying to draw. | [
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If you scribble it so quickly that we can't tell if the back of the input side is round or straight and you scribble the front side so we can't tell if it's pointy or round, then we won't know what it is. Just do it carefully enough that you can tell those two things and then people can tell what you're trying to draw. All right, what about not? So not zero? Not one? Good. Okay, so a bunch of ways we write not. | [
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All right, what about not? So not zero? Not one? Good. Okay, so a bunch of ways we write not. We'll stick to usually the first two. So we'll put a prime when we don't have any video graphical writers handy or chalkboard. Often we'll write a bar over it. So the bar or the prime means complement not. There's also mathematical complement, which is this little thing here. So you might see that in some texts. | [
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There's also mathematical complement, which is this little thing here. So you might see that in some texts. The not gate is a triangle in an inversion bubble. The thing that actually does the not part is the circle. Okay, so if you see it without the circle, that's actually just a buffer. Okay, so it just repeats the signal that's used for performance reasons in circuits. So it's the circle that does the inversion and sometimes people will draw circles all by themselves. | [
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Okay, so it just repeats the signal that's used for performance reasons in circuits. So it's the circle that does the inversion and sometimes people will draw circles all by themselves. So in the book, in the Pat and Patel textbook, you can find still a few diagrams where there are inversion bubbles on the inputs to gates. So those are actually nots and if you built it, you'd have to have a gate for each of those little circles. | [
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So in the book, in the Pat and Patel textbook, you can find still a few diagrams where there are inversion bubbles on the inputs to gates. So those are actually nots and if you built it, you'd have to have a gate for each of those little circles. And they'll fix that in the third version, but the third version, they're trying to save you money because the publisher wants them to produce versions. | [
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So those are actually nots and if you built it, you'd have to have a gate for each of those little circles. And they'll fix that in the third version, but the third version, they're trying to save you money because the publisher wants them to produce versions. I really shouldn't say this too much on video. Anyway, so when the third version comes out, those will go away. But for now, if you're looking at the current edition, they still have some of those inversion bubbles on inputs. | [
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Anyway, so when the third version comes out, those will go away. But for now, if you're looking at the current edition, they still have some of those inversion bubbles on inputs. All right, what about XOR? A, zero XOR zero? Good. Zero XOR one? One XOR zero? One XOR one? Good. All right | [
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I really shouldn't say this too much on video. Anyway, so when the third version comes out, those will go away. But for now, if you're looking at the current edition, they still have some of those inversion bubbles on inputs. All right, what about XOR? A, zero XOR zero? Good. Zero XOR one? One XOR zero? One XOR one? Good. All right. So usually we just write that a plus sign with a circle around it and it looks like OR when we draw it as a gate, but it has two lines on the input side. | [
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All right. So usually we just write that a plus sign with a circle around it and it looks like OR when we draw it as a gate, but it has two lines on the input side. Sometimes the inputs will cross the first line. Sometimes they won't. It doesn't make any difference. Those mean the same thing. So that's an XOR gate. To generalize, use the definitions that I gave you. So AND is the all function, OR is the any function, XOR is the odd function. | [
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To generalize, use the definitions that I gave you. So AND is the all function, OR is the any function, XOR is the odd function. We just looked at two inputs. If you want to use more inputs in order to make them commutative and associative, they're defined this way. Okay, so let's do an example with three input XOR. So it's the odd function. So what's zero XOR zero XOR zero? Good. Zero zero one? Zero one zero? Zero one one? One zero zero? One zero one? One one zero? And one one one? Good. | [
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So what's zero XOR zero XOR zero? Good. Zero zero one? Zero one zero? Zero one one? One zero zero? One zero one? One one zero? And one one one? Good. So again, if you look at these, I mean, I think people are mostly following along, but it is the odd function, right? The number of ones on the left, if it's one or three, you get an output of one. If it's zero or two, you get an output of zero. | [
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So again, if you look at these, I mean, I think people are mostly following along, but it is the odd function, right? The number of ones on the left, if it's one or three, you get an output of one. If it's zero or two, you get an output of zero. And you can generalize to four or five, ten input XOR if you'd like. I won't draw the truth table. All right. So there's another way that we generalize these functions, which is by pairing up bits. | [
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All right. So there's another way that we generalize these functions, which is by pairing up bits. So a lot of instruction set architectures on computers, and even starting maybe Friday or the day after Labor Day next Wednesday, you'll start to see these operations in the C language where you can take two sets of bits and do a Boolean operation on them. So for example, we might write something like this here, C equals A and B, where A is an n-bit number, bit pattern. | [
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So a lot of instruction set architectures on computers, and even starting maybe Friday or the day after Labor Day next Wednesday, you'll start to see these operations in the C language where you can take two sets of bits and do a Boolean operation on them. So for example, we might write something like this here, C equals A and B, where A is an n-bit number, bit pattern. B is an n-bit bit pattern. | [
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So for example, we might write something like this here, C equals A and B, where A is an n-bit number, bit pattern. B is an n-bit bit pattern. And what we mean by this A and B, where I've written it out with the word, is to take those bits, line them up. So you take A sub n minus 1, B sub n minus 1, you AND those together using a two input AND, that produces C n minus 1. You do that for all of your values of I, and what you get is this number C, where it's a bitwise AND between A and B. | [
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] |
So you take A sub n minus 1, B sub n minus 1, you AND those together using a two input AND, that produces C n minus 1. You do that for all of your values of I, and what you get is this number C, where it's a bitwise AND between A and B. So this is what you typically use in a computer where you've got names representing sets of bits, and then you might AND whole sets of bits together. | [
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You do that for all of your values of I, and what you get is this number C, where it's a bitwise AND between A and B. So this is what you typically use in a computer where you've got names representing sets of bits, and then you might AND whole sets of bits together. So it's another way to generalize the idea of the Boolean expressions, or the Boolean functions that we've talked about. | [
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So this is what you typically use in a computer where you've got names representing sets of bits, and then you might AND whole sets of bits together. So it's another way to generalize the idea of the Boolean expressions, or the Boolean functions that we've talked about. Be careful not to mix the algebras. So when we talk about bitwise operations, we usually use the words. The reason is that it can get confusing, because when we talk about sets of bits, we can do things like plus. | [
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