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[MUSIC]. 

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Let's go back to our road map and look at 
the next topic that we'll be covering. 

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we're going to focus next on integers and 
floats, the representation of numbers in 

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in memory. 
That's going to be an important precursor 

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before we can man, look at all the 
instructions for manipulating that data 

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values. 
So this section is going to cover the 

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representation of integers. 
Both signed and unsigned. 

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And how we treat integers and c. 
talk about some shifting and signed 

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extension operations that will be 
important for arithmetic. 

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And then we'll close with a section on 
floating point numbers. 

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basically, how do we represent binary 
numbers that are fractions rather than 

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just integers? 
And then, we'll get into a little bit of 

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detail on the IEEE floating point 
standard for floating point numbers. 

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And how we do floating point operations. 
And the rounding that they entail. 

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As well as look at floating point numbers 
and see. 

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There's a lot more to floating point 
numbers. 

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And we, we'll leave a lot of those topics 
to the text to cover. 

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but we will do some of the basics. 
But before we get to integers Just wanted 

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to talk about a encoding problems in 
general. 

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So suppose we have a 52 card deck. 
A, you know, the typical playing card 

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setup with 13 cards of each suit 
organized into four different suits. 

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and we want to figure out how to 
represent these in binary numbers how do 

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we use zeros and ones to represent all 
these cards, well we could start by 

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thinking about the operations we want to 
be able to do on the cards so we probably 

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want to be able to tell if a card is 
higher than another. 

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or if they're the same suit that might 
help us think about the kind of encoding 

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we have, lets take a look at some 
examples, so heres a very simple encoding 

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to start with we have 52 different cards, 
so lets use 52 different bits, with bit 

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corresponding to the card that we haev 
set to one. 

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So that would let us use 52 bits of a 64 
bit word, let's say. 

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In what's called a one hot encoding. 
And meaning that there's only going to be 

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one bit set to one, all the others will 
be set to zero. 

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So we can have the first bit represent 
lets say the ace of clubs. 

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Okay and the next bit represents the two 
of clubs and so on. 

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What are some of the drawbacks to this? 
Well it's going to be really hard to 

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compare values and suits because we have 
individual bits throughout those 52. 

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where we have to look for the value in 
the suit of the card and we sure have a 

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large number of bits to represent 1 card 
an entire 64 bit word. 

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This is called a 1 hatting code where 
only 1 bit is on another possibility to 

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do do a 2 hotting coding where we might 
use 4 bits to represent the suit and 

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another 13 bits to represent the 13 
possible values of the card. 

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So now two bits would be set to one. 
So the fir-, the first bit in the suit 

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might be set, to indicate the suit clubs 
and the, the first bit in the value might 

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be set to indicate an ace. 
okay. 

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So now it's a lot easier to tell if two 
cards are of the same suit, because 

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they'll have the same 4 bits here. 
And, we can tell, if a card is greater 

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than another, by looking at the position 
of the 1 in the remaining 13 bits. 

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But that's still a bit cumbersome. 
It's easier to compare suits and values 

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but it's still a large number of bits. 
in this case 17. 

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This is what's called a two-hot encoding 
now, because we have two bits set to one 

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for each card. 
Let's continue with this exercise and 

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look at two possibly better 
representations. 

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we could just do a binary encoding of all 
52 cards, we only need 6 bits to 

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represent 64 diferent numbers so we can 
take care of 52 in just 6 bits, that 

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would allow us to fit a card into just a 
bit and use the low order 6 bits to do 

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that. 
So that's kind of nice. 

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It all fits in one byte. 
and it's much smaller than the one or 

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two-hot encoding. 
But how can we make the value comparisons 

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easier? 
the suit comparisons easier. 

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we're still going to have all the cards 
numbered from one to 50 bit, one to 52, 

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and that will not make it easy to do 
those comparisons. 

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so we can do something that's a bit of a 
hybrid, we can use two bits for the suit, 

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four bits for the value. 
Two bits for the suit because we have 

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four possible suits, so we need four 
possible binary bit patterns here, 00, 

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01, 10 and 11. 
One and then four bits for the value. 

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Because the card can be anything from an 
ace to a king 13 different values. 

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Okay so this makes it now easy to still 
do that suit comparison, and just check 

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if a number is smaller or greater than 
another take away the value. 

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Okay. 
So, let's take a look at how we would 

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implement these operations if we were 
doing it in in C. 

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So, if we wanted to check if 2 cards are 
of the same suit, what we would do is 

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have 2 bytes representing each card, 
Okay? 

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Maybe an array to represent a five card 
hand. 

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We would take two cards out of the hand 
and ask if they're the same suit. 

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And this function sameSuitP is 
implemented here below. 

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It returns a boolean value just zero or 
one. 

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And takes the two cards as, arguments. 
What it does, you'll notice, is, it takes 

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the first card, and does a bit wise and 
with the suit mask. 

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What is the suit mask? 
The suit mask is a special value set to 

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hex 3, 0. 
Why hex 3, 0? 

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Well that corresponds to 00110000. 
You'll notice that when we do a bit wise 

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and with this mask, we will only have non 
zero results for these two bits. 

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All the other bits will necessarily be 
zero. 

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Because we have a 0 here and 0 ended with 
anything will result in a 0. 

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So this will essentially extract the 
value of the suit form the card 

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representation. 
It will only have a nonzero value 

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possibly in these 2 bits okay. 
So, then we can do an exclusive OR with 

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the suit of the other card. 
Okay and why do we do an exclusive OR? 

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Well remember, an exclusive OR says 
either one is true or the other is true 

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but not both. 
Okay? 

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So, we would only get a perfect zero 
result If these two suits matched 

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exactly, in other words, they had the 
same zeros and ones in these two 

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locations, if they have that, then the 
result will be all zeros. 

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And that's a bouillon false, and by 
taking the complement of it logically, we 

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can say then that, tho, those two cards 
match. 

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That our result is true. 
Okay. 

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So what we actually implemented here was 
the opposite of the x or by using the 

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not. 
In otehr words, we said, rather are the 

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two suits different bits. 
We, we're asking, are they the same bits? 

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By just doing the compliment of the X0. 
All right, that would have been the same 

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as saying this using the equals, equals 
boylean operator that says these 2 things 

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exactly match I just showed you what we 
could do with the boylean operators 

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Alright. 
Let's take a look now at comparing the 

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values of two cards. 
Again we have our array of five cards, 

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our hand. 
And we compare two cards, card1 and 

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card2. 
So which has the greater value? 

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Is card1 a greater value than card2? 
So you'll notice here what we're going to 

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do is Apply a different mask to the card. 
This mask is value 0f, the value mask. 

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It has a one in the low order four bits. 
So we're getting f-, the low order four 

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bits, which represent the value and 
zeroing the suit. 

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And the way we get the suit zeroed is by 
applying the logical AND with a mask that 

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has zeros in these positions. 
So now the result won't necessarily be 

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there and if we compare 1 of those 
extracted values to the other we can 

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simply get the greater relationship 
between the 2.