00:00 Hello, my name is Oyase Sunday. I'm taking you to Mathematics JSS 3 class. We have an interesting topic for today.

00:20 A topic is subtraction of numbers in base two numerals. A subtraction of numbers in base two numerals.

00:27 That would be under basic operation of the binary system or the binary numbers.

00:32 Now the binary numbers have numbers expressed in base two. And so, and it would not exceed zero and one.

00:45 And don't know now we'll be doing the subtraction of this operation.

00:50 That the question is, I don't know the class, what are we expecting? Now at the end of the class, we'll be expecting to solve subtraction of two three digits of binary numbers, subtraction of two three digits of binary numbers.

01:05 And understand the basic operation in subtraction. Subtraction adds its own roots, the basic roots that must be followed while carrying out a subtraction.

01:16 Now, what are binary numbers? The question is, what are binary numbers? Now, binary numbers are numbers that are similar to base ten.

01:27 But except these numbers are expressed in base two. And the numbers must not exceed zero and one.

01:39 Numbers between the range of zero and one are called the binary numbers. Now, these are numbers that consist of zero and the two digits, zero and one.

01:51 Now, for the subtraction of binary numbers, to be effective enough, you need to follow what we call the basic roots or binary numbers, the basic roots.

02:03 We call them the four roots of the binary number, the four good in roots. And what are the four roots? The four roots of the binary numbers phase number one, zero minus zero.

02:19 Zero subtracted from zero gives zero.

02:24 One. That's your topic. It becomes very, very important. Two. One subtracted from zero. That's one minus zero is equal to one. Very important.

02:42 Three. Says one minus one is equal to zero. Very important. One minus one gives zero.

02:56 Then the four two, which is called the root of exemption, that's the four two, that we have zero minus one. It's not zero minus one. It's not possible.

03:11 So we have to borrow. So in this room, we will need to borrow. Now, what do you need to do? You borrow from the nest digits. So this is where the borrow comes in place.

03:27 So please take notes that when we have zero minus one, it is time to borrow. We will be borrowing from the nest digits. So we could complement it and carry on your question.

03:39 One zero minus zero gives zero. One minus zero gives one. One minus one gives zero. And zero minus one is not possible. But we have to borrow. When you borrow one, we are expected to have one.

03:59 After examining this four rules of subtraction, there is a need for us to be able to solve questions. Applying these four rules, soft questions, applying the four rules become very, very important.

04:16 Let's move to question number one. It is evaluate zero zero one one zero one zero minus zero zero one one zero zero.

04:35 Evaluate zero zero one one zero one zero minus zero zero one one zero zero.

04:47 Take note. What do you need to do first? Write the right values out. So I have example one. I have zero.

04:57 Zero one one zero one zero. And zero zero one one zero zero zero to zero. So I have I'm subtracting.

05:19 Take note of the four rules. So obey the four rules becomes more easy obey the four rules. Now zero minus zero one zero minus zero gives zero.

05:37 One minus zero one minus zero gives what one? But zero minus one. That's the rule. That is the exemption zero minus one. That's the rule. That's the exemption.

05:52 What do you need to do? You borrow one from here. You borrow one. The one leaves here and comes here to say plus one.

06:04 So you're transferring this one to this place. So this one out. Not then is left there. So it goes straight to this point.

06:13 So when when it is coming here. It's not coming here as one. It's coming here as the base. So take note. When it is coming it's coming as it's a plus.

06:24 But when it's coming it's a plus one. But it appears here as plus two. That's the base. It appears as plus two. So take note of it becomes important.

06:37 It's not appearing here as a plus one. But what plus two? So we now have yeah is not longer zero. What is left? What is not here is two. So two minus one. What do you have?

06:51 One. Now remember this is off. So I'm having here as zero. That is left here. So is there?

07:03 Minus one. It's not possible. We bought a problem. So we bought one from here. So this out comes here. I'm having it as plus one.

07:16 But when it comes here it becomes plus two. Now I've been not a plus two. So yeah it's already out to be zero. So what do I have?

07:26 So I have two minus one. I have it as one. What is left here is zero. So zero minus zero gives me zero.

07:35 Zero minus zero gives me zero. And the last one gives me zero. So my answer.

07:44 How? Take note of the bowing. The bowing becomes the key. If you bow out of this place, the value is no longer there.

07:54 The value has been transferred to the next point. But it's transferring to the next point as the base. So when we are bowing, take note of that.

08:02 So my final answer gives me zero zero zero triple one and zero. Let's take another example which we called example two.

08:14 Now take notes of these fours. Take example two. You have example two. I have zero one.

08:29 Zero zero zero one zero. And I have zero one zero one zero zero zero subtracting.

08:50 Let's subtract out. What are we expecting to have? So I have just note of the who. Zero minus zero. That gives me zero.

09:04 One minus one gives me zero. Remember zero minus zero is zero. One minus one is zero.

09:23 One minus zero. One. Then is zero minus one. You bow. You bow your one. So following the rules, let's go. Zero minus zero will have as what is zero.

09:38 Now zero minus one is a minus minus one. Remember it cannot be bow. Looking at the next value is zero. You can't bow from zero because zero there's nothing there.

09:50 Look, next value after is one. So I bow one. So the one is out here. It's transferred. It cannot go straight to the next two value. So it goes to the next.

10:02 It goes here as plus one that becomes plus two plus one becomes plus two. So take note plus one becomes plus two. So it goes here becomes plus one and plus one is plus two.

10:25 Now why is it plus two? It's plus two because we are transferring in relation to the base. That's plus two. So mean that what we have here is not longer zero. So this is there it out.

10:40 What we have there is now plus two. Plus two. Now remember we are going to this digit, which is the fourth digit. Now to the fourth digit.

10:52 So I still need to transfer one. Bow one from this to I say, hey, give me one. So it gives me one. That's plus one. And the plus one is coming here as plus two.

11:10 It means that the year is left with only one. Only one. Just note becomes important. Take note of those. That's manipulations in the figure making it flexible to use. So I have plus two.

11:25 Plus one coming at the base as plus two. So I have two. So there is already out. So I have two minus one. Two minus one. That gives me one.

11:37 Now I have one left here. Remember I have one left here. And I have one minus zero. Remember two about a one minus zero. That gives me what? One minus zero gives me one.

11:53 What is left here? Left here is zero. So zero minus zero gives me zero. And zero minus zero gives me zero. So my process is complete.

12:06 Remember I had to go to a third digit to bow. And when I was bowing, it comes into text my one out of my two return. It becomes two. So when bowing the flexibility in it is when transferring when you are transferring, you have to be very, very careful.

12:28 Now, take another example. This is evaluates. We have evaluates. And there is a decimal point in the third question. The decimal point is introduced here. That's example three.

12:46 we have evaluate, I have evaluate 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, so I have 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

13:16 1, 0, 1, 0, 1, so I have subtraction.

13:30 So I have many digits that I have before the point,

13:32 take note of the digit before the point.

13:34 I have digits after the point, digits after the point,

13:38 or before the point, take note of the one before the point,

13:41 and one after the point, but the one that is more important

13:43 is the digits after the point.

13:46 So we have two digits after the point.

13:48 I have one, one, I have one, 0.

13:52 So I have, I'm in the digit, I have one, two, three, four, five, six.

13:56 One, two, three, four, five, six, seven.

13:59 One, two, three, four, five, six, seven.

14:01 Seven before the point.

14:04 Two after the point.

14:06 After the point is vital.

14:08 So I don't want to have one, two, three, four, one, two, three, four.

14:13 So I have, so, one, two, one, two, three, four, five, six, seven.

14:17 How do you go about it?

14:19 So, okay.

14:20 Now you could see that I could rearrange it in a way I decided to.

14:25 Or let's take, let's take off this.

14:27 So I have, one, minus, zero.

14:30 Remember our rules.

14:32 One minus, zero.

14:33 What do you have?

14:34 That gives us what?

14:35 One.

14:37 I have, one minus, one, that gives us zero.

14:42 I have, one minus, one, that gives us what is zero.

14:47 I have, one minus, zero, that gives me one.

14:52 I have, zero minus, one.

14:55 Not possible.

14:56 I bow one from here to this place.

14:59 It becomes plus one that becomes out and become plus two.

15:04 You remember this one is out of the equation.

15:08 So I have two here.

15:09 The zero two is out.

15:10 So I have two here.

15:11 So I have two minus one, that gives me one.

15:15 Remember, yeah, it's let with what is zero.

15:18 So I have zero minus zero, I guess we're zero.

15:21 So I have one minus one, that gives me zero.

15:25 I have one minus, zero, that gives me one.

15:30 And I have one minus one, that gives me zero.

15:34 So take it off.

15:35 But the point, the point is two digits after.

15:40 So you can't the first two digits.

15:42 One and zero, I put your points here, in between.

15:47 So it becomes a more clear and a more steady to go about.

15:52 Question number four.

16:01 Is it evaluates?

16:02 Evaluate?

16:04 Question number four.

16:07 Is it evaluates?

16:09 One, zero, one, zero, zero, one.

16:15 And I have one, zero, zero, one, one, one, one.

16:20 Take it off.

16:24 Subtraction.

16:25 Follow your four basic rules.

16:26 By now, I'm expecting that you are familiar with the four rules.

16:30 Four rules, I have zero minus zero, give zero.

16:34 I have one minus zero, gives one.

16:39 I have one minus one, gives zero.

16:43 And I have zero minus one, you want, but you have to vote.

16:48 So familiarize yourself with the four rules.

16:50 So with this, every step processes can be easy to go through.

16:53 So let's go with this.

16:54 We have one minus one, I have zero, zero minus zero.

16:59 I have zero, zero minus zero.

17:01 I have zero, one, one minus one.

17:07 I have, now if you take note of it very well,

17:09 you would observe that you have, you have zero, yeah.

17:14 So most times I can take off the zero.

17:16 I can just take off the zero.

17:18 That is zero in this corner.

17:19 I'll say, okay, what do I have?

17:22 I have, take it off.

17:25 I have, looking up it,

17:30 I have one to three, zero, zero.

17:32 And I have one zero, okay.

17:36 That's three zeros, three zeros.

17:38 Three zeros at the top.

17:41 Three zeros.

17:43 And I have one, one.

17:47 I have, or three zeros at the top.

17:52 Two zeros, I have one.

17:57 And I have zero, and I have one, okay.

18:02 So going back to the process again, I have a half,

18:09 one minus one, zero, zero minus zero, zero,

18:12 zero minus zero, we give it zero.

18:14 Now, zero minus one, no, it's cannot go.

18:18 We have to borrow, borrow one from here,

18:20 take it off, yeah, it becomes plus one out becomes plus two.

18:26 So this is zero is already out to two minus one,

18:29 that gives us one, yeah, it's left with zero.

18:32 And the zero minus one, not step possible,

18:34 we have to go and borrow.

18:36 Are you, we can't borrow from zero,

18:37 we have to go and borrow from one.

18:39 So you borrow from one, you send it here, that becomes,

18:42 if you send it here, that becomes plus two,

18:46 no longer zero, plus two, you send one of the two here,

18:50 that becomes plus one, becoming plus two.

18:54 So two minus one, that gives us one, one.

18:58 So we have, what is left here?

19:00 Yes, already taking out, which is zero.

19:02 Yes, already taking out, then zero is left here.

19:04 So I have one, yeah, minus one, that gives us zero.

19:07 So zero, zero, zero, all true.

19:09 So I could just leave my answer in this form,

19:11 because zero, zero, zero, before it does not really matter.

19:14 So now looking at it very, very well,

19:17 we'll move straight up, it has given us

19:19 and a clear ability on how to solve the questions.

19:23 Following the four basic rules, that is,

19:25 zero, minus zero, equal to zero, one, minus zero,

19:31 one, one, minus one, zero, and zero, minus one,

19:35 it cannot, you have to borrow one from there.

19:39 Having understood the four rules with the examples,

19:42 it is time to take our evaluation class.

19:45 Now, evaluation class.

19:48 Question number one says, evaluate, triple 1, 1, 1, minus 1, 1, 1, triple 0, 1, evaluate,

20:04 1 1 1 minus 1 1 triple 0 1 2 evaluate 1 0 0 1 1 minus triple 1 1 1 evaluate 1 0 0 1 1 minus

20:30 triple 1 1 1 thank you very much for watching come to the end of the class my name is

20:36 oya say sunday till next class