Base Two Arithmetic

Added: 2026-05-30

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[00:09:45]All right. Today we are looking at an interesting topic based to arithmetic and this is something that we must have started doing right from primary school but today we want to make it as simple as possible for every one of us. So by the end of today's class, B 2 arithmetic will be or should be a walk over for you. There should be nothing in B2 arithmetic that you should not that you will not be able to do.

[00:10:24]For instance, you should be able to know how to convert between base two number and base 10 number. So conversion either you're converting from base 10 to base 2 or from base 2 to base 10. So after today's class, you should know that like the back of your finger.

[00:10:46]Then you should know how to do basic operations. What do I mean by basic operations? Things like adding, subtracting, multiplying base two numbers.

[00:10:58]Just the way you add, subtract, multiply base 10 numbers. You are aware of base 10 numbers. She started using B 10 numbers right from primary school right from NOS in fact. So today we want to look at base 2 arithmetic. Okay.

[00:11:20]Now as I said we started using B 10 numbers right from primary school from even nursery. And for base 10 which is the normal counting number we have 10 digits. We have only 10 digits in base 10 numbers. And what are the digits? 0 1 2 3 4 5 6 7 8 and 9. These are the 10 digits we have in these 10 numbers.

[00:12:04]So if you want to go beyond nine then you start combining these digits. If you go beyond nine you have to combine these digits to get the number you want. So for instance to get the next one which is 10 you have to now combine 1 and zero. So you have 10. To get the next one which is 11, you combine one and one which is 11.

[00:12:32]To get the next one which is 12, you combine one and two. So you keep combining after you exhaust the first 10 digits.

[00:12:45]So you can see that the numbers in base 10 have or the digits we have are 0 1 2 3 4 5 6 7 8 9 that is for base 10 but we have other counting or sorry we have other numbers in other bases.

[00:13:09]So for counting normal counting we use base 10. But when you come to computing like when you come to computer language programming what computer understands is the base two or binary system where we just have two digits 0 and one. So in base two we only have just two digits zero and one. So in base two number you can't see two you can't see three you can't see any of these digits after this one after zero and one. So if you get if you go beyond one then you start combining just the way if you go beyond nine for base 10 you start combining these digits to form that number. So if you go beyond one, you have to now start combining zero and one to form whichever number you want to form after one for base two counting.

[00:14:15]Do you understand? All right. So for instance, if you want to get the next one after one, you know, you won't write two because the only digits that is in base two number is 0 and one. So what do you do?

[00:14:34]You have to combine this and this. That will give you 1 Z. Now how do you get 1 Z? This is the way you get 1 Z. So the next one after one is supposed to be two. But since you can't write two, what you would do is to divide two by the base we are considering which is base two. Right? So 2 / two you'd have one remainder 0. 2 by 2 is one remainder 0. So you write one and then zero.

[00:15:10]So that's how we get 1 0. Then the next one you know what the next one will be which is three. But since you can't write three you say 3 / 2 this will give you one remainder one. So it means what you're going to write here instead of three would be one one.

[00:15:30]So this is how you form numbers in base two counting. And remember I said in base two where we apply it is in computing computer language programming and all of that. Okay.

[00:15:46]So but we can change between base 10 and base 2 and I'm going to show you how to do that and that will be the first thing that we'll do. How to change from base 10 to base 2 and then how to change from base 2 to base 10.

[00:16:05]Let's go.

[00:16:07]Let's start with changing from base 10 to base 2.

[00:16:22]Let me start with this one. So I want to change 32 base 10 or 32 b 10 to base 2.

[00:16:34]I want to change three to base 10 to base 2. How do I do it? Now, if you want to change from base 10 to any other base, all you need to do is to keep dividing that number.

[00:16:48]Keep dividing whatever number you have there that you want to change. That is the number in base 10. Keep dividing by the required base. So, for instance, this one we have 32 base 10. We want to change it to base 2. So we keep dividing by two. Do you get? So let's divide 2 into 3 that will be one remainder one into 12 that will be six. No remainder.

[00:17:16]So you you write remainder zero. There's no remainder. So you write remainder zero. So you keep dividing. 2 into 16 is 8. Is there remainder? No. So you write remainder zero. 2 into 8 is 4. Is there a remainder? No. So you write remainder zero. 2 into 4 is 2. No remainder.

[00:17:40]So you keep dividing. You keep dividing.

[00:17:42]2 into 2 is 1. There's no remainder. 2 into 1 is zero. Remainder one. So you have to divide until you get to zero. Do you get? You divide until you get to zero.

[00:18:00]When you get to zero, you read up the remainder from bottom up like this. So it means 32 base 10 32 base 10 in base 2 will be 1 0 0 0 base 2. So you can write it out as the like this 32 base 10 is equal to 1 0 0 0.

[00:18:28]How many zeros? Five base two.

[00:18:36]So you can see we can't write 32 in base 2 like this because we don't have the digit three in base 2 and we don't have the digit two in base two. So we have to break it down into zeros and one. It has to be only a digit zero and one that you can write in a base two number.

[00:19:02]Do you understand? Good. So you're going to do one for me.

[00:19:08]You're going to change.

[00:19:10]So we are still changing from base 10 to base 2. You're going to change for me 47.

[00:19:19]Change or convert 47 base 10 to base 2.

[00:19:28]Change 47 B 10 to base 2. Let me know your answer in the comments.

[00:19:39]Let me know your answer in the comments.

[00:19:42]So, remember what we said we we you're going to do. You keep dividing by two.

[00:19:49]noting the remainders. So when you get to zero, then you now read up the remainder from bottom up. So he's doing that for us.

[00:20:01]First person to get it gets a shout out.

[00:20:06]47 B 10 to B 2.

[00:20:21]47 B 10 2 B 2 I've not done this so I would I will do it with you guys.

[00:20:32]47 B 10.

[00:20:36]All right. So, Mario says 1 0 1 1.

[00:20:42]That is four ones base two. Mario.

[00:20:47]Okay.

[00:20:48]Mario. Well done. I'll check if you're correct.

[00:20:54]Um, David says one one base 2. Same thing with what Mario said. All right.

[00:21:05]Well done.

[00:21:11]Okay.

[00:21:12]One one one Ibraim.

[00:21:16]Ibrahim says one one. Am I getting something different from Sabira? Okay.

[00:21:23]She has deleted it.

[00:21:26]Okay. One11 base 2. Paulina. Paulina says the same thing um Mario, David and Ibraim have said. All right, that would mean maybe that's the correct answer. We going to check it.

[00:21:44]All right. Uh Kenny says 1 1 0 011 is two H.

[00:21:52]That's different from what others have gotten. All right, we're going to check if you're correct.

[00:21:58]All right. Someone say um deep bassi deep basi says 101 one one base two same thing others um have said earlier. Okay that's cor that's good. 1011 one11 base 2i adi.

[00:22:27]Okay, cheese. All right, we are all saying almost the same thing. Let's see if you guys are correct.

[00:22:35]Let's see. So, we have 47.

[00:22:39]Someone says he doesn't understand. So, listen carefully as I explain this.

[00:22:44]Okay. So, we keep dividing. If you're changing from base 10 to any other base, keep dividing by that base you want to change to. So, in this case, we want to change to base two, right? So we keep dividing by two. 2 into 4 is 2. No remainder. 2 into 7 is 3 remainder 1.

[00:23:07]So we skip dividing by 2. 2 into 2 is 1.

[00:23:10]2 into 3 is 1 remainder 1. 2 into 11 that will be 5 remainder 1. 2 into 5 that will be 2 remainder 1. 2 into 2 is 1. There is no remainder. So we write remainder zero. Then 2 into 1 is zero remainder one. So we have to read up from bottom up like so.

[00:23:41]So when you get to zero, you stop and read up the remainders from bottom up.

[00:23:47]So that 47 B 10 will be equal to would be equal to one. We are reading from bottom 0 1 one one one base 2. Awesome. So most of us got it from from David Mario Ibraim. Most of you got it. Well done.

[00:24:14]That's very good. So, we've seen how to change from base 10 to base 2. How about if you want to go back like for instance, you have this and you want to go back from base 2 to base 10. How do you how do you do it?

[00:24:35]How do you do it? All right, I'm going to start with a smaller number with a smaller one instead of like this long one to show you how you change from base two back to base 10.

[00:24:49]How you change from base two back to base 10. So for instance, if I have 1 1 0 1 base 2, I want to change it to base 10.

[00:25:07]There are other ways you can see something like equation like this in the exam.

[00:25:13]This one is from um junior y or if you call it in your school b convert 1 01 base 2 to denary.

[00:25:27]This is another way to say base 10 denary.

[00:25:32]Base two is binary.

[00:25:36]Okay, binary. But base 10 is denary.

[00:25:40]So you might see something like this denary. So you don't get confused. What they mean is base 10. Okay. So convert 1 1 0 1 base 2 to base 10.

[00:25:53]How do we do this? The first thing you need to do is to label the digits. So starting with the one on the rightmost side that is this particular one you start labeling it as 0 1 2 3 0 1 2 3. So if the digits continue you continue as well to label it 4 5 6 7 like that. So once you label it then you can multiply. So we would say this is equal to one. We are actually expanding the digits one that is this one times the base this base raised to power the label raised to power the label like this. So you are done with this one. You move to the next one. 0 you say + 0 * the base raised to power the label we are changing from other base to base 10. So what we are doing for base 2 can be applied to any other base. So if you want to change from base 7 to base 10 is the same process that I'm doing now that you also apply. If you want to change from base 5 to base 10, the same thing. So 0 * 2 raised to power 1 plus we move to the next one which is this one. 1 * the base raised to power the label the label here is two right plus finally 1 * the base which is two raised to power the label. The label is what? Three.

[00:27:47]So we have expanded this and whatever we get after doing this expansion will be the number in base 10. It will be the number in base 10. So let's go.

[00:28:03]2^0 is what? Anything raised to power 0 is 1. Anything raised to power 0 is 1.

[00:28:09]So 1 * 1 that will give us 1. So we are done with this 2^ 1 is 2 * 0 anything * 0 is 0. So we have + 0.

[00:28:25]So we are done with this.

[00:28:29]Moving on 2^ 2 power 2 is 2 * 2. What is 2 * 2? 4. So 4 * 1 is 4. So we are done with this.

[00:28:42]And then finally 2^ 3 is 2 * 2 * 2 which is 8. 2 * 2 * 2 is 8. Now 8 * 1 is still 8. So we are done with this. So we say + 8. So when you add up 1 + 0 is 1 + 4 is 5 + 8 is 13.

[00:29:10]So we have 13 b 10. So instead of writing 13 like if you want to write it in base 2 the equivalent of 13 is 1 0 sorry 1 1 0 1 base 2. So these two numbers are the same thing.

[00:29:33]13 B 10 or 1 1 0 1 base 2. These are equal numbers. They are the same numbers. So you've learned how to change from base 2 to base 10.

[00:29:53]If you have actually learned it, then you're going to do this for me. So you see the procedures. First of all, we label the digits. Starting with the rightmost digit, we label it as zero and keep going like that. 0 1 2 3. Then after labeling, we now expand. Starting with this one, we say 1 * the base raised to power the label. 1 * 2 raised to power 0. we move to the next digit which is 0 and we say 0 * the base which is 2 raised to power the label. So we keep doing that until we exhaust the digits and then we we simplify whatever we have add them up and that will give us the number in base 10. Okay so if you understood that then let's go with this one. you're going to change from me. This is a longer one, but it's is easy actually. Convert 1 0 1 0 1 base 2 to base 10.

[00:31:14]So I can call it base 10. I can call it denary. Okay.

[00:31:19]convert 1 0 1 0 1 base 2 to base 10.

[00:31:23]Another way I can call it is decimal decimal. Decimal benary um base 10 all mean the same thing. So in case you see any of these expressions in maybe your exam or you see it anywhere you know they talking about the same thing which is base 10.

[00:31:45]So who is doing that for me quickly?

[00:32:03]Who is getting this for me? Who will be the first to get it? The first person to get it gets it. Shout out pass.

[00:32:23]Oh, so we are already getting 21. Fumi Lion says 21 B 10.

[00:32:30]Okay. Wow. This class is awesome. We're getting it so fast. David says 21 B 10.

[00:32:37]Okay. Steven says 21 B 10. Blessing 21.

[00:32:43]Okay.

[00:32:45]Oh, someone says 23. Okay. Let's see who's correct. 23.

[00:32:52]Adi Wally. Adi Wally says 23. Okay. 23 B 10. Vivian says 21 B 10. Okay. Vivian.

[00:33:09]Um, someone says he's 13. Is that Mumus?

[00:33:17]Mumus says he's 13.

[00:33:20]13. Do you mean 13 B 10?

[00:33:24]Okay.

[00:33:27]Paulina says 29 B 10. 29. We are getting different answers. Cham says 21 B 10.

[00:33:35]Okay. Cheese.

[00:33:37]Um 21. Christristiana says 21.

[00:33:49]Rachel.

[00:33:50]Rachel says 21 B 10. Okay. All right.

[00:33:55]Many of us says 21 B 10. Some says 29.

[00:33:58]Some said 23.

[00:34:01]I think I saw one that said 203. All right. Let's see who is correct.

[00:34:06]Remember what we said we are going to do. We first label the digit starting with the rightmost one which is this. So we label it with zero 1 2 3 4. Now after labeling the digits what do you do next?

[00:34:23]You now expand. Right? So um we start with one. We are expanding this one. we say 1 multiplied by the base which is 2 raised to power the label.

[00:34:42]The label is zero plus the next one is zero. Now if I was like the one solving it myself I will not do this. Once I see zero as a digit I will just keep it because at the end of the day anything you multiply by zero will still be zero. Do you understand?

[00:35:04]So, but let me just write it because I'm teaching. So, 0 time the base, which is 2 raised to power the label. The label is 1 plus the next one 1 * the base raised to power the label. The label is what? Two. Plus remember I said if you're solving on your like you're solving you don't need to write this zero because it will still give you zero so no need writing it but let's write it because I'm teaching 0 * the base raised to power the label the label is what three then finally this one 1 * the base the base is 2 raised to power the label which is 4.

[00:35:55]Good. Now let's add up. Let's simplify.

[00:36:00]Starting with this one. 2^0 is what? 1.

[00:36:04]Anything raised to power 0 is 1. 1 * 1 is 1. So we are done with this. Let's move to the next one.

[00:36:13]2^ 1 2^ 1 is 2. Then time z is zero. So that's why I said for these ones I wouldn't have written it if I was solving on my own. Then I'll move to the next one. 2^ 2 is 4 and 4 * 1 is still 4. Good. Then I'll move to the next one which is this 2^ 3. 2^ 3 is 2 * 2 * 2 which is 8. 8 * 0 is 0.

[00:36:51]Okay. Then plus the last one.

[00:36:55]The last one 2^ 4 is 2 * 2 * 2 * 2 which is 16.

[00:37:01]16 * 1 is still 16.

[00:37:05]So when we add what are we going to get?

[00:37:08]1 + 4 is 5. 5 + 16 is 21.

[00:37:15]So most of us got it. 21 base 10.

[00:37:20]So the equivalent of 1 0 1 01 base 2 in base 10 is 21. Do you understand? So you can see how we change between different bases. So if you are writing 21 as a base two number, this is how you are going to write it. This one here. And if you want to write this 1 0 1 0 1 as a base 10 number, this is the way you are going to write it.

[00:37:55]What that means is that if you write 21 in computing like you type 21, what the computer understands as 21 is 1 0 1 0 1 because it will convert it back to base two because the computer understands only binary numbers 0 and one. Is that clear? Good. So, we've learned how to convert between bases. Now let's go on to basic operations.

[00:38:29]In maths we have different types of operations. The basic ones are addition, subtraction, multiplication, division.

[00:38:45]These are the basic operations in mathematics. So we want to know how do you add in other bases like how do you add a base two number is it the same way you add in base 10 how do you subtract a base two number is it the same way you subtract in base 10 that's what we want to know in this section okay so quickly I'm going to be adding let's start with addition I'm going to be adding 1 0 1 one.

[00:39:19]This is in base two. I'm adding it to 1 1 0 1.

[00:39:29]So this is the addition I want to do.

[00:39:33]And of course I will leave my answer in base two. So let's add.

[00:39:37]Pay close attention so that you don't miss it. Once you get the the concept behind it, it doesn't matter how big the number is, you will always get the answer because it's just about the concept, the understanding. So don't be distracted. Just pay close attention. 1 + 1 is what? Is two.

[00:40:04]But would you write two? No. Why?

[00:40:08]because you are only working you are working in base two and it only contains the digits 0 and one. So you can't write two.

[00:40:18]What do you do instead?

[00:40:20]This is what you do. Remember what I said earlier. You have to now divide by the base. This will give you one remainder zero.

[00:40:31]You might not know that this is what you are doing in base 10 addition. You might not know but this is exactly what you are doing in B 10 addition. Because for instance, if you want to add this 30, let's say 39 + um + 14.

[00:40:52]This is in base 10. If you say 9 + 4, what do you normally do? You say it's 13, right? But would you write 13 here?

[00:41:03]No, you don't write 13. What do you do?

[00:41:06]You say write three and carry one, right? But you didn't know that this is what you actually did. What do I mean?

[00:41:18]That 13 you got eh? You say 13ide by 10. This is one remainder three.

[00:41:27]Okay.

[00:41:30]So you are actually writing the remainder which is three and then taking this one to the next place value.

[00:41:38]That is what you are doing. But you we you are not taught that this is the step you actually took because it's very easy to divide by 10.

[00:41:49]Anytime you divide by 10, of course, it will be the first digit that will be what 10 goes into and then the remainder will be the next digit. That's why we just say write if you get 13, write this and carry the next one to the next to the place value.

[00:42:09]But this is actually what you did in base 10. This is what you are doing unknowingly. I'm sure you didn't know that this is what you're actually doing.

[00:42:18]But for base two and any other base, you have to consciously do it.

[00:42:24]So that's the only um difference between adding in base 10 and adding in other bases.

[00:42:33]You do it. It's the same thing you are doing but unconsciously you are just doing it because that is like the way you were trained from maybe primary school. You write if you have 13 you simply write three and carry one. That's what you told. But this is exactly what you did. You divide by 10. This is one remainder three. So that's why you are writing three and carrying one to the next place value. So that's what we are going to be doing here because you can't just for instance you get two. You might not know what to write here.

[00:43:10]You might not know what to write. So you have to now do the division like consciously that's the only difference.

[00:43:18]The fact that you have to divide by the base consciously is the only difference between adding in base 10 and adding in other bases. So 2 / two we have one remainder zero.

[00:43:33]So what we are going to write will be this remainder and then we take the this one to the next place value. Do you understand? So 1 + 1 + 0 is still two. So we have already done the division for 2. 2 / 2 is 1 remainder 0. So we still write the remainder which is zero and take one to the next place value. 1 + 1 is two.

[00:44:00]We've already done the division for two.

[00:44:01]So we know that what we are supposed to write will be zero. So we take 1 to the next place value. Then 1 + 1 + 1 is 3.

[00:44:12]So you've not done division for three.

[00:44:14]So we have to divide 3ide by two is one remainder 1. So we have to write this one the remainder and then take this one to the next place value. But since you don't have anything here, you just bring that one down.

[00:44:32]You get it? So we have one 1 0 0 0 base 2.

[00:44:40]This might look as though it's hard hard, but it is not. It's exactly what you are doing with base 10. The only difference is that you you are unconsciously doing this division because it's very easy to divide with 10. You're unconsciously doing it. But now you have to consciously do it because you are dividing with other bases. You are not you are not used to them. Do you understand?

[00:45:07]All right. So let's go over it again.

[00:45:11]1 + 1 is two. But we wouldn't write two.

[00:45:15]Why? Because two is not a digit in base two number. We only have zero and one.

[00:45:23]So because of that we have to divide two by two. This will give us one remainder zero. We write the remainder which is zero and then take one to the next place value. So that's what we kept doing until we got our answer. Now you will do this for me.

[00:45:44]One one one is two. You're adding it to one one 0 1 base 2 and you're also adding it to 1 0 1 base 2. Do this addition for me.

[00:46:11]Remember 1 + 1 + 1 is 3. But you can't write three, right? You know what to do.

[00:46:17]So do it and let me know what you get.

[00:46:33]who gets the answer first.

[00:46:46]This class is just one to three and yet some people don't know some people are behaving like they in primary primary school.

[00:47:01]So you come to a live class like this and all you can do is chat.

[00:47:10]It shows you're not a serious student.

[00:47:14]I don't have time for those kind of students.

[00:47:20]Someone says 212 binary. 212. I don't get that.

[00:47:26]What is 212 binary?

[00:47:39]What is the answer for for four?

[00:47:46]I don't get that as well. What's the answer for four? What What do you mean?

[00:47:53]All right. Angela says 1 1 0 0 is two. Okay, Angela, we are going to check if you're correct. I doubt that you are, but let's see.

[00:48:09]Okay.

[00:48:13]1 1 1 01 1 1 1 01.

[00:48:20]Okay, that's awesome. Let's see if you're correct. Uh Vivian says 1 0 01 B 2.

[00:48:30]We are getting very different answers.

[00:48:34]Uh Mr. theorist says 1 0 01 base 2. All right. You know what? When I solve it, then you'll know if you are correct. But do well to put your answer down. Okay?

[00:48:48]Do well to put your answer down.

[00:48:51]Um I can see Chin Chin says 1 0 01 is two. Same thing with Vivian.

[00:48:58]Okay.

[00:49:00]Um or here, sorry. Or here go lights.

[00:49:02]Gosh lights.

[00:49:05]Okay.

[00:49:07]Yeah. If your name is different from what appears as your username, always add your name to your answer. Okay.

[00:49:18]All right. I can see 1 0 0 1.

[00:49:23]Um Amaz 0 three zeros then one.

[00:49:30]All right. We getting so many different answers. Let's do it together.

[00:49:35]So let's add 1 + 1 + 1 is 3. But would you write three? This is a base two number. You only have 0 and 1. So you can't write three. What do you do? You have to divide three by two. You say 3 / two. This will give you one remainder one. It is the remainder that you will write. Then then this one you have to take it to where the next place value.

[00:50:02]Do you understand? So now 1 + 1 that will be two. So you can't write two as well. So you have to say 2 / two. This is one remainder zero. Again it is the remainder that you would write. Then this one you take to the next place value. So you have this.

[00:50:24]Now 1 + 1 + 1 + 1 is four. Would you write four? No. You have to divide four by two. This will give you what?

[00:50:36]This will give you two remainder zero. So you have to write the remainder only the remainder you write.

[00:50:46]Then you take two to the next place value.

[00:50:51]So let's go. 2 + 1 + 1. 2 + 1 + 1 is four. What would you do? You will not write four. You have to write zero.

[00:51:01]Right?

[00:51:03]and then take two to the next place value. So we got four right? So we say two remainder zero. You write the remainder which is zero and then take two to the next place value. So you are writing two in this place here.

[00:51:23]Now why we we will not just write two like we did for the last one here is because two cannot be a digit in base two number. So what do we do?

[00:51:37]You divide again by two. We already divided by two before. So two 2 / two is one remainder zero. So we write the remainder zero and take one to the next place value. We don't have anything here. So we just write that one down.

[00:51:59]This class is amazing. I think many of us got the answer. 1 0 0 0 1 base 2.

[00:52:09]Wow. This class is amazing.

[00:52:13]Okay. Collins one 0. Yeah, Collins got it.

[00:52:19]got it. Many of us got it. Wow. Cham got it. I think Oh, here go light got it as well.

[00:52:31]But not all of us got it anyways.

[00:52:34]I think um the I think where we started um getting it wrong is around this place where we got four or something like that. Maybe around here. But you you see how we how I explained it, right? So we got four around here, right? 2 + 1 + 1 is four.

[00:52:56]So we say 4 / 2.

[00:52:59]This will give us two remainder zero. So we write the remainder which is zero here. Then this two we take to the next place. But we can't just write two. We say 2 / 2.

[00:53:14]This will give us one remainder zero. So it's this remainder zero that we write.

[00:53:19]Then take this one to the next place value like that. So if you keep dividing and the number you you need you took to the next place value is still bigger than zero and one.

[00:53:35]What do you do? You keep taking you keep dividing and writing the remainder. Keep taking it to the next place value like that. Do you understand?

[00:53:45]So if for instance we get a very big number like six, you keep dividing like 6ide by two. You say three remainder zero. Okay? You write zero carry three to the next place value. You divide.

[00:54:02]So in in reality what you are doing is you are changing this six from base 10 to base 2. Anyways let's move on.

[00:54:15]I think this will be the last one because of time.

[00:54:21]I will just take subtraction as the last one because of time. So let's move on to subtraction. We are still dealing on basic operation with these two numbers.

[00:54:37]1 1 1 0 B 2 - 1 0 1 1 base 2. How do we do this subtraction?

[00:54:53]Subtraction. Okay, pay close attention.

[00:54:56]You do subtraction just the way you do subtraction in base 10, but you see a bit a little bit different.

[00:55:05]So 0 minus one cannot go. What do you do? Normally in base 10, you say you borrow one from the next place value, right? And that one will make this 10.

[00:55:17]But that is because you are working in base 10. Anything you are boring is actually 10.

[00:55:25]But if you are boring in base two number, what you are boring is not 10 but two.

[00:55:32]If you're working in base three number what you are borrowing is not 10 but three. So but now we are working in base two. So that one I borrowed from this one here will be two not 10. That is the difference. So now we have 2 minus one. That one can go. So we have one. All right. But this one that I borrowed one from will now be zero. 0 - one cannot go. So I have to borrow again from this one. So this will be this will now be two. Right? So we have 2 - 1 is 1. Now this one will be what? 0 because I bled one from it. 0 - 0 is 0.

[00:56:18]1 - 1 is 0. So we can rewrite this as 1 1 2. You know that any if you have zero before in any number you have like zero maybe I have 0 02 this thing is same thing as two if it is in front of the if it's in front of two then this whole zero doesn't mean much. So you can you can remove this 0 0 but if it is behind it like 0 0 then this is 200. You can't just remove this. You understand? Good.

[00:56:56]So our answer is 1 1 base 2.

[00:57:03]Now do this for me. This will be our last one. Subtract subtract 1 1 b 2 from 1 one 1 0 b 2. Subtract 1 one one b two from this.

[00:57:23]So the first thing you have to do is to know how to arrange what how would you arrange this if you're subtracting then do the subtraction and let me know what you get.

[00:57:38]This our last one.

[00:58:04]Or here says 1 0 1 1.

[00:58:09]Are you answering this one? 1 0 1 1.

[00:58:13]Okay. I don't know if you're correct.

[00:58:17]I've not done it.

[00:58:20]David says one one B2. One one B2.

[00:58:25]All right.

[00:58:27]Says 111 B2.

[00:58:31]One. Okay. EV says 111. Wow. Okay. Most of us are getting 111. Let's see if you guys are correct. This is our last one.

[00:58:44]And I hope you guys are correct.

[00:58:49]Let me do it. Okay, let's do it together. So, we want to subtract this from this. How would you arrange this?

[00:58:57]First of all, you bring So, this is the one you put on top, right? Because you're subtracting this one from it.

[00:59:07]So, this base two minus, you know, when you're subtracting, you have to know how to place a digit in in the proper order. You don't start writing this like this. This will be wrong.

[00:59:25]You have to start from the unit place. So this will be the right way to write to make this arrangement.

[00:59:35]Okay. So once you make the arrangement, you should be able to get the answer 0 minus one. It cannot. So I have to borrow right. I have to borrow from one.

[00:59:47]This will become zero. And I'll take that one here. Now, but that one you borrowed is actually a base two number.

[00:59:55]So, that number is two, not 10. 2 - 1 is 1.

[01:00:04]0 - 1. You can't, right? So, you have to borrow again. So, I'm borrowing from this. This will be zero. Now, this will be two. 2 - 1 is 1. Now, this is already zero. So, you cannot you can't subtract one from zero. So you have to borrow again. This will be zero. And that one you borrowed is actually two. 2 - 1 is 1. And so we are done. 1 one is 2.

[01:00:35]Almost all of us got the answer. Wow.

[01:00:37]This class is amazing.

[01:00:39]All right. That's it for today.

[01:00:43]Um I didn't explain that of multiplication, but it's almost the same thing. It's almost the same thing with what you what I've explained for addition and subtraction.

[01:00:57]So, let me know how was today's class.

[01:01:03]How was today's class?

[01:01:20]How was today's class?

[01:01:33]All right. Um, Wanda says it was very good. Uh, Chin says it was great.

[01:01:40]Fantastic. Amazing.

[01:01:43]All right.

[01:01:45]I loved it. Chin says she loved it.

[01:01:50]I don't mind them. They kept fighting, but it was great. I don't have their time, so I I just neglect them. All right. They are very unserious students.

[01:02:03]Okay. It was amazing. It was interesting. Today's class was amazing.

[01:02:07]And I loved it. All right.

[01:02:13]Fantastic. Fum is just fantastic. Okay.

[01:02:18]All right. Someone is asking for assignment. Um. All right. Let me let me do something.

[01:02:24]You know, I didn't explain that of multiplication, but like I said, it's almost like the same thing. Okay. So because I I'll give you something a bit difficult.

[01:02:37]So in the next class you should ask me for the answer. So let's go calculate 1 1 0 b 2 * 1 0 1 1 b 2 + 1 0 0 1 b 2 - 1 0 1 b 2.

[01:03:04]This is it. You ask for assignments.

[01:03:07]This is it. So in the next class you let me know what you got so we solve it together. Okay. So I would use that opportunity to explain multiplication.

[01:03:18]But like I said multiplication, addition, division, um subtraction, they are almost like the same thing. I'm sure you guys will get this answer. But let's see in the next class. All right. This is where we say bye-bye. If you are not subscribed, click on the subscribe button right away. so you don't get to miss any of our lessons. Okay, click on the subscribe button right away.

[01:03:48]Until next time.