00:00 Hello, my name is Oyase Sonday. I'll be taking you madmatis jsS3 class. We're looking at an interesting topic for today that says multiplication of numbers in base 2 numerals, multiplication of numbers in base 2 numerals.

00:29 That is part of the basic operations we have in the binary. Remember, the binary operations have addition, subtraction, division, and multiplication.

00:44 Then the last one we have expected is to convert, but the basic operations around is addition, subtraction, division, and multiplication.

00:56 So, what is the class? What are we expected at the end of the class?

01:01 Now, the objective of the class is to solve multiplication of 2 to 3 digit binary numbers, how to solve, how to go around questions that involve 2 to 3 binary digits.

01:17 So, how do you solve them using multiplication? And understanding the basic operations in multiplication of numbers in base 2.

01:26 How do you go around the operation of numbers in base 2? That becomes very, very important.

01:32 Now, the first question is what are both binary numbers? What are binary numbers? What makes binary numbers different from every other numbers?

01:43 Now, binary numbers are, they work similar to base 10, they work similar to base 10, but the exception is this, binary numbers are expressed in 0 and 1.

02:03 That is, they're expressed within 2, the framework of 2 digits. And what are the digits? 0 and 1.

02:16 Now, within the framework of these 2 digits, we have the binary numbers.

02:20 So, our question that will be carried out, that all the digits that we'll be given,

02:25 text notes will be the digits between 0, combination of 0 and 1. Now, when we want to carry out the multiplication, the question is,

02:36 if we decide to carry out the multiplication of binary numbers, do we just go without following some basic rules?

02:43 There are basic rules to follow when you are carrying out multiplication of the binary numbers. What are the basic rules?

02:50 1, a rule. The rules are quite simple, I have 1, 0 multiplied by 0 gives 0.

03:01 1, 0 multiplied by 0 equal to 0, rule 2, 0 multiplied by 1 equal to 0.

03:17 That makes it easy, it makes it easy to walk around with, rule 3, I have 1 multiplied by 0 equal to 0.

03:28 Now, makes it more easier. So, if I don't have the last two without the thoughts and I have 1 times 1 equal to 1, so I don't need to borrow.

03:40 So, the interesting about the multiplication is you don't need to borrow, you don't need to borrow, just multiply it through.

03:46 For why multiplication is a little bit advanced than addition and subtraction,

03:55 is that multiplication, most often multiplication, brings in addition, multiplication of binary numbers,

04:04 do not just stand on their own, they bring in addition alongside with it. So, these are the four rules,

04:13 0 multiplied by 0, 0, 0 multiplied by 1, 0, 1 multiplied by 0, 0, then 1 multiplied by 1 is 1.

04:23 As I want to say, okay, solve, I have 1, 0, mean 1, 0, okay, 1, 0, 1, 0, and I have 1, 0, 1, I'm multiplying.

04:44 Now, let's multiply in the multiplication. It becomes important that you use your first digits.

04:53 First to digit goal, not the three. So, I have 1 times 0, 0, 1 times 1, 1, 1 times 0, 0, 1 times 1, 1.

05:06 Now, picking a next digit, 0, 9 digit is 0. Now, go, 0 times 0, 0, you pick the first to digit

05:19 aside. 0 times 1, 0, 0 times 0, 0, 0, 0 times 0, 0 times 1 is 0.

05:30 Bring it out. You are adding. Now, you are not processing. Remember, you are addition.

05:36 Addition goes. So, in addition, what do you have? Bring the 0 comes down. This one comes down.

05:48 0, 0 plus 0, that's 0, hmm? Okay, so we have 1 plus 0, 1. There we have 0, and the 0 can continue.

06:01 Okay, so we have this. But there is still one more process left. One more process does this,

06:09 which is called the one. So, let the one goes now. One time this. You remember, you have started,

06:16 you have left 2. So, you're starting, you've left 2 first to start from the third, you get it.

06:22 So, you've left 2, you're starting from, you've left 2, you're starting from where?

06:27 The fourth. 1, 2 has been left. So, you're starting here. There have 1 times 0, 0, 1 times 1, 1,

06:40 1 times 0, 0, 1 times 1, 1, 2. Now, you're adding. Adding up. So, when you're adding up, what do we have?

06:52 We had up. This one comes down, 0. This one comes down, 1. This one comes down as 0. They are not

07:01 tampered with. But 0 plus 1, I have 1, 0 plus 1, 1 plus 0, 1, 0 plus 0, 0 plus 1, 1, and then we have 0,

07:18 yeah, and bring out your final one, 1. So, you could just have it in this form, yeah.

07:28 Now, let's take up another question to give us a better and a clearer idea of how to solve the

07:38 multiplication. So I have example two. I have a half zero one zero zero one one zero one

07:57 multiply. Now going to this process it's it's easier so let's take it up. So what do we have?

08:05 Remember before digit one times one one times one sorry one times one one

08:13 one times zero zero one times zero zero one times one one it's easier. Remember you leave the first two

08:24 zero times this leave the first two oh it's one so I have the do value is one one so I have one

08:36 times one let the first two deeply the first digits one times one one one times zero zero one

08:46 one times zero zero one times one one so I'm looking ahead and we have the addition of digits

08:59 addition of the digits now what do we have when you have them up what do you have in this one comes

09:05 down the zero comes here now I have okay now you would observe that I have one one

09:19 I have one zero zero one okay now look up I leave a space let me look top

09:30 I leave a space I left a space that I left a space for one zero zero one

09:48 so I left a space so I have a addition I have okay one I have I have zero plus one one zero plus

10:06 zero zero one plus zero one then I have one but still let's flip up the space

10:20 okay now we still have this left how do you take care how do you take care of it you multiply it

10:32 now let's go so when you multiply it techniques that when you multiply it that appears on that

10:38 so I have one times one I have that's what one remember I leave the first two digits one times zero

10:46 zero one times zero zero one times one one so I have one one one zero plus one one one plus zero one one

11:02 one plus zero one one one then fine now one that's is my finances so I have one one one one one one one

11:15 now this gives you an idea of what to expect to expect now it means that it should be able to work

11:23 around it working around it gives you a better process on how to solve questions relating to it

11:32 Okay question number three question number three now says solve so we're solving one

11:38 zero zero one and I have one one one multiplying now I have one times one one one times zero

11:51 zero one times zero zero one times one one okay now you go for the next one times one you don't

12:02 take it under the first you move to the next one times one one one one time zero zero one time

12:08 zero zero one times one one now you are adding up now when you are adding up you have

12:17 this gives us one that is coming down zero plus one that's one zero plus zero zero zero

12:26 zero one plus zero one then one remember there's two one one operation to perform that is

12:33 this one at the left so you're multiplying one times one on that in nest now you need you need

12:40 more space so you leave the second space you start one times one one one times zero zero one

12:48 times zero zero one times one one you are adding now why adding up to be

12:57 answer that will give us yeah bring out the one now bring out the one then the zero plus one

13:07 bring down the one one plus zero bring down the one one plus zero bring down the one then the

13:15 final one is one all in base two okay now we have we have all in base two okay so we have

13:29 this as this at the final answer because we have three values that is one one it would so if we're

13:40 having it four values if it was a four value then we would have had an addition to this so we have

13:50 zero one if it's a four value you go down to have another one that can become your final answer

13:56 so if you had that last value to eat let's make it a four value from the question making a four value

14:01 so I have this really top taking this last one yet really top from the question so adding a one

14:10 value to eat I have one times zero remember you let the two space for the first one then now you're

14:17 going to live in one two three three space so the fourth one one time zero one times one one zero

14:25 aha then you have for the last value you are multiplying the initials I was the initial

14:34 the initial is one zero zero one that's your multiplying by one this one this one

14:43 so one times this one times one one one times zero zero one times zero zero one one so taking it

14:52 down I'm going to be having one zero zero one so final answer you are adding up so add up

15:02 I have one one it's coming down one now one plus one that's two so that's two divided by two

15:12 that gives us one remainder zero that's one remainder zero now that's one remainder zero that's one

15:21 so we have zero take out one so I have at the one the one is transferred to this place

15:30 to give us plus one so one plus one that's two we turn back here that's zero then I have one again

15:40 transferred to this place so that gives us plus one yeah plus one one plus one that's two

15:48 we turn back here that gives us zero that what do I have then I have the last one

15:55 transferred yeah that's plus one so plus one plus one that gives us two we turn back here

16:06 that's give us zero one as a final answer okay now that gives us zero one a final answer now with

16:17 this one two and three questions we've been able to evaluate all what we need about the division

16:25 now we're going to be taking an evaluation evaluation says evaluate one one one one that's two

16:32 four one one multiply by one zero one evaluate one zero zero one one multiply by one one one

16:42 thanks for watching my name is Oyase Sonde till next time