Binary, 2's Complement and Hexadecimal

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Course
Time
13 hours 15 minutes
Difficulty
Beginner
CEU/CPE
14
Video Transcription
00:01
Hello. This is Dr Miller, and this is Episode 1.4 of Assembly.
00:06
So today we're gonna learn about binary two's complement and Hexi Decimal
00:11
binary.
00:13
So, by near is what a computer uses in order to store numbers. And it uses ones and zeros,
00:19
and each bit represents a powers of power of two. So we have to to the 0 to 2 the one to do the two and so on and so forth until we get to to to the seven.
00:29
So to do the zero represents the number one. And then we basically doubles to go down the line. 1248 16 32 64 128.
00:40
And when we're converting, we basically add up all these numbers in order to get our decimal number.
00:45
So, for example, if we have the number 33 we're gonna go on down the line until we get to a number that is smaller than the current number that we have. So we have 33.
00:54
Well, I don't need 100 28. I don't need 64 but I do need a 32
00:59
and then we go ahead and subtract the two. So 33 minus 32 gives me one, and I can kind of shortcut and go down here toe one to say I do also need a one.
01:07
And so the number 33 would be 00100001
01:14
That would be its binary representation.
01:18
To convert from decimal, we take on binary number. We go ahead and write it down, and then we just right above it all of the powers of two.
01:26
And everywhere I have a one that means I want to include that.
01:29
And so I need a 128 plus 32 plus four plus one
01:34
by Adul those together I get 165. So the number 10100101 is 165 in decimal
01:46
two's complement.
01:48
So two's complement is what computers use in order to store both positive and negative numbers. And the top bit or most significant bit represents a sign.
01:57
So if we see a zero, that means that this is a positive number. If we see a one, that means that this is a negative number,
02:07
so we're gonna convert from decibel into two's complement. If the number is positive, we just convert it from decimal into binary like we did before.
02:15
If it's negative, we're going to convert our number two binary and then we're gonna flip all the bits. So every zero becomes one and everyone comes a zero,
02:24
and then we'll go ahead and add one to that. And that is the process to convert from decimal two two's Complement
02:32
to convert from two's complement to decimal.
02:36
So we have a binary number. If the most significant bit is a zero. We just converted to decimal, so it's a positive number. We just go ahead and convert it like we did before.
02:45
But if the most of name Gigabit is a one, we're going to convert it to binary.
02:49
Then we'll flip all the bits ever again. Every zero becomes the one everyone becomes zero,
02:53
and they were gonna add one,
02:57
and then we'll converted to decimal. But we got to make sure at the end that we add a negative sign to say that this number is a negative number.
03:06
So here's some binary addition, fax. So we got zero plus zero. We get zero, and I added a leading zero here.
03:14
One plus zero is 10 pose. One is one.
03:17
One plus one is two. But we're writing in and buying areas. We've got a zero
03:23
ones and we got one too. So we got 10
03:28
and then one plus one plus one is 11.
03:30
I mean that you can go and tell your kindergartner that one plus one plus one is 11 and see what they think.
03:38
So, for example, if I have the number and negative 42 well, it's negative. So I'm gonna go ahead and cover 42 to binary. So I need a 32 and an eight in a two. So I get to move my binary number and then we flip all the bits so you can see that every zero becomes a want and everyone becomes a zero.
03:58
And then we add one clear to the end, right? So
04:00
I have this, I say, plus one. So one plus one gives me
04:05
10 and all the rest of the bits remain the same.
04:10
And so negative. 42 in two's complement. Is this number right here? So 11010110
04:21
Hex or Hexi Decimal.
04:24
So Hexi Decimal is based 16 and it allows us to represent binary numbers using the letters zero through nine and a through F.
04:35
And so we can see the
04:36
binary representation and then the hex number.
04:41
So again, this is just converting from binary to decimal will give us all zeros to give us zero or, for example, six.
04:47
So I got a 1248
04:50
So I got two plus four will give me six
04:54
within, For example, we got the number 10. So let's 10. 10 or an eight in a two. And that gives us the letter A
05:02
all the way through F Right. So one plus two plus four plus eight.
05:08
Well, give us 15.
05:10
And so one bite is gonna go ahead and be to Hexi Decimal dishes. Digits.
05:15
So again, we have the process of taking the number 42. We already did the first part of the process,
05:20
right? So I converted that in two's complement, and I got this number, this number down here
05:29
and I put a space in here so that we could see the hex digits relationship so
05:32
you'll go ahead. And if you're converting that into from
05:36
the number negative 42 decimal two two's complement using Hex,
05:43
go ahead and do the whole process to convert to two's complement. And then we got to convert toe hex.
05:46
So I will take my number 1101 Go ahead and look it up in my table and it looks like 1101 is a D.
05:55
And then I look up my other number. 0110
05:59
I believe that is a six. And so the hex representation is
06:03
zero x. So this is the prefix we generally use for Hexi decimal numbers
06:09
and then d six.
06:12
So that represents the number
06:14
negative 42.
06:18
So now if I'm given the number zero x A and I'm going to convert that from Hexi Decimal two's complement into
06:28
binary star decimal.
06:30
So we take the number a A and we convert that from zero ac from Hexi decimal into binary.
06:36
So a is 1010 I'm gonna have another 11010
06:43
Then I flip all the bets. So every zero becomes one. Everyone becomes a zero. I go ahead and add one again. One plus one is 10. So I have my Carrie,
06:53
and then I go ahead and I convert this into binary. So looks like I have a 64 plus a 16 plus a four plus a two.
07:01
So I add those all together that gives me 86. And we remember that we started off with a one right that told us that we needed to convert it.
07:10
And so that means that this number is negative. 86
07:14
and in decimal form.
07:18
So in summary today, we talked about binary two's complement and then Hexi Decimal as a representation.
07:27
Looking forward, we were going to talk about instructions and then logical operators.
07:32
If you have questions, you can contact me at Miller MJ at you and Kate. I e to you. And you can find me on Twitter at at Milhouse 30
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