00:00 Hello everyone, I am Esther Oluchi, your Mathematist teacher, and the topic of today's

00:22 lesson is "Conversion of based and numerals to binary numbers."

00:30 By the end of the lesson, you should be able to convert based and numerals to binary numbers.

00:39 In our previous lesson, we looked at counting in group of tools, where 9 was group in tools, using the counter,

00:47 on the paper abacus as shown below.

00:51 And we arrived at grouping the number 9 in base 2, we have 1, 0, 0, 1.

01:01 So in this lesson, you will be able to understand better how we arrived at that.

01:06 And now there are two methods of converting numbers in base 2 to base 2 numbers.

01:11 And the first method is subtraction method, what is second method is successive division method.

01:22 Now, let's solve this example, convert based 5 based 10 to base 2 number.

01:29 So, how do we solve this question?

01:32 You have to be familiar with the powers of 2.

01:35 To be able to convert numbers from base 10 to numbers in base 2,

01:40 you have to be familiar with the powers of 2.

01:44 So, 2 to the power of 0 equals 1 to the power of 1 equals 2 to the power of 2 equals 4.

02:05 2 to the power of 3 equals 8.

02:15 And also 2 to the power of 4 equals 16.

02:30 And now we are given the number 5.

02:37 Okay, now these are the powers of 2.

02:41 So, if it is good, you get familiar with them as you convert numbers in base 10 to base 2.

02:48 Okay, now we are given number 5 to convert to base 2.

02:54 So, we have 5, let's draw power, or write that sometimes, we decide to make it this way.

03:02 Okay, now we are given the number 5 to convert number in base 2.

03:08 So, we have powers, let's start from the less group of 2s to 8 to group of 2s.

03:14 We have 4s, we have 2s, then we have 1.

03:18 So, we are given the number 5.

03:21 Remember in our previous lesson, we counted these numbers, then we decided to group them in 2s, then in 8, and so on.

03:28 So, for number 5, using the subtraction method, we look at our paper abacus and check 8.

03:37 This 5 does not get up to 8, like 8 as 6/5.

03:42 So, we move to the next number on the paper abacus, which is 4.

03:46 Okay, with 4, with 4, we can have 4 in 5.

03:49 So, we subtract 4 from 5.

03:54 So, we have 5 minus 4, giving you 1.

04:02 So, from here now, it means that we have a 4 in 5.

04:07 So, what do we do? We write 1 here, 4, 5, then we have 1 left.

04:14 So, I remember right now, the next power is 2, but we know that 2s is 1.

04:25 So, we can have anything here, because it's not possible, we get 2 from 1.

04:30 And 1 is what we have left after subtracting 4 from 5.

04:34 So, sometimes for us to better understand, we do this.

04:39 Or we draw an arrow, better still, like we have on this slide.

04:46 4.

04:49 So, we have 1 left. So, for this, there's nothing, we have 0 here.

04:54 So, the 1 that we have here, there's a 1 here.

04:57 So, we just put down 1 here, there's a 1 here, add your 1 here.

05:04 So, we see that this 4 plus 1 equals 5.

05:09 So, the binary equivalent of 5 in base 10 equals what?

05:14 It's very clear now, we can see that on the board.

05:19 5 in base 10 equals 1, 0, 1 in base 2.

05:27 You can see 1, 0, 1 in base 2.

05:32 Okay, let's move on.

05:35 Example 2.

05:37 Convert 10 in base 10 to base 2 number.

05:41 How do we do this?

05:43 The same method, using the subtraction method.

05:52 So, let's write all, let's draw a...

05:57 Okay, let's better still group them into 2s.

06:00 Because we have 8, we have 4, we have 2, then we have 1.

06:08 So, we have number 10.

06:13 From number 10, what number we can see here?

06:15 We can have 8 here.

06:17 So, what we do?

06:18 We'll say 8, 10, minus 8.

06:22 What do we have?

06:24 We have 2 left.

06:29 We have 2 left.

06:31 That means, in 10, we can have an 8 in 10.

06:34 So, we have 1 here.

06:39 4, 10.

06:40 So, we have 2 left.

06:42 So, look at that 2 now.

06:44 We see that 4, the next number on this upper course is 4.

06:48 Well, look at that.

06:49 We see that 4, 8, 6, 2.

06:52 So, there's no way we can write 1 on the 4 for 10.

06:56 So, we skip that, or better still, we write 0.

07:02 So, we have 2, we can see that we have 2 here, and we say 2 here.

07:06 So, we write 1 for that.

07:08 That means, that's all.

07:09 That means, for 10, we have 8, we also have 2.

07:14 That's nothing more, because 8 plus 2 gives us 10.

07:17 So, for 1, that's nothing there, so we have 0 here.

07:21 So, it means, also, that the number 10 in base 10 equals 1, 0, 1, 0 in base 2.

07:38 You can see, if we subtract 8 from 10, we have it there.

07:42 The next I's number just on the 2 is 2.

07:44 So, we write 2.

07:46 Make sure that the 2 numbers, 8 and 2, add up to 10.

07:54 So, a number 10 in base 2 is 1, 0, 1, 0.

08:00 So, let's look at example 3.

08:02 Convert 7 in base 10 to a number in base 2.

08:09 Okay, now let's solve example 3, which says, Convert 7 in base 10 to a number in base 2.

08:16 So, let's do that also.

08:19 We have 7, example 3, 7 in base 10.

08:28 Let's draw the numbers on our paper abacus.

08:41 We have 8, we have 4, we have 2, then we have 1.

08:47 So, 7 is not even up to 8.

08:49 So, there's no need of words counting or trying to write 1 under 8.

08:58 Don't be need for us to do that.

09:00 So, let's count, there's no need of counting this time, Asian.

09:02 So, a special method.

09:03 So, notice that the next number after 8 is 4.

09:06 So, what do we do?

09:07 We subtract 4 from 7.

09:10 So, we have 7 minus 4, given us word 3.

09:16 So, write 1 here under 4, because there's a 4 in 7.

09:23 So, we have 3 left.

09:24 So, how do we do this?

09:25 We can do this.

09:26 The next number immediately after 4 is 2.

09:29 So, under 3 here, we see that 2 does not exceed 3.

09:34 So, there's a 2 in 3.

09:36 So, what do we do?

09:37 The same thing here, 3 minus 2, given us 1.

09:41 That means, well, I don't get 2.

09:43 Because, we have 1 left here now.

09:46 So, what do we have?

09:47 We also have 1 left.

09:48 So, just put it there.

09:49 We have 1.

09:51 So, that's the answer.

09:55 7 in base 10.

09:58 7 in base 10 equals 111 in base 2.

10:04 Very simple.

10:05 So, let's move on and see what we have left.

10:09 Now, example 4, using successive division method.

10:13 Convert 5 in base 10.

10:16 10 in base 10.

10:18 7 in base 10 to numbers in base 2.

10:21 We have done this using this subtraction method.

10:24 I'm using the same number so that we can see for ourselves that,

10:27 whichever method you use, you arrive at the same answer.

10:30 That's the essence of me.

10:31 Repeat the same numbers so that we can use another method to solve them.

10:35 To see it for ourselves that, whichever method we decide to use,

10:39 we're going to arrive at the same answer.

10:41 So, let's begin.

10:44 So, how do we use successive division method?

11:01 For me, which one we did, I know you were here, we did SCM and SCM.

11:05 This is our line.

11:06 It's the same thing we're going to do.

11:08 The same line we use in doing SCM and SCM.

11:10 That's the same line we're going to use in solving, trying to convert base 10

11:15 to base 2 using the successive division method.

11:19 So, for the number 5, let's do this.

11:25 We draw our line.

11:28 We write the number here, 5 here.

11:31 They write our base here, 2 here.

11:33 So, we divide.

11:35 After the division, we're going to divide it.

11:37 We get nothing left.

11:38 So, now, we'll say 5 divided by 2.

11:40 What will it give you?

11:41 2.

11:42 Remember what?

11:43 Remember 1.

11:44 You'll come here again, 2.

11:46 Same 2.

11:47 2 divided by 2.

11:48 1.

11:49 Remember what?

11:50 0.

11:51 So, there's the number here.

11:52 You will stop.

11:53 You have 0 here.

11:54 Then 2 here.

11:56 OK?

11:58 Now, 2 divided by 1 is 0.

12:01 Remember 1.

12:03 So, we're going to draw an arrow like this.

12:06 Because we're going to be counting from bottom.

12:09 We're going to be writing from bottom to the top.

12:11 That is from the most significant bit to the least significant bit.

12:16 So, we have our answer that is 5 in base 10 to be equal to what?

12:23 1.

12:26 0.

12:27 1 in base 2.

12:30 Start from here.

12:32 So, it seems to be the same here.

12:34 But don't start from the beginning.

12:36 Start from the bottom.

12:37 That's where the arrow goes from here to the top.

12:52 The second one, which is the bit part, 10 in base 10 to number in base 2.

12:59 So, we draw a line also here.

13:01 We convert our 10.

13:03 Write your 2 here.

13:04 10 divided by 2.

13:05 We give you 5.

13:06 Remember what?

13:07 0.

13:09 5 divided by 2 again.

13:10 2.

13:11 Remember what?

13:12 1.

13:13 Write your 2 again.

13:14 2 divided by 2.

13:15 We give you 1.

13:16 Remember what?

13:17 0.

13:18 Then again.

13:19 2 here.

13:20 So, 1 divided by 2 was 0.

13:22 Remember what?

13:23 1.

13:27 So, we can see that 10.

13:32 10, in base 10.

13:35 Don't forget that you are supposed to come to write from the bottom to the top.

13:41 Now, we have 1, 0, 1, 0 in base 2.

13:46 You can see that this is what we got when we even used the subtraction method.

13:50 We got the same answer.

13:51 So, whichever method you feel you like or it's convenient for you, you're free to use.

13:59 So, the last example is 7 in base 10.

14:07 Okay, now let's solve the last example, which is 7, base 10.

14:12 Then we ask to convert your number in base 2.

14:16 The same method, the successive division method.

14:20 So, let's go draw a line.

14:23 7 here.

14:24 2 here.

14:25 7 divided by 2, giving you 3.

14:27 Remember 1.

14:29 2 here.

14:30 3 divided by 2.

14:31 Giving you 1.

14:32 Remember 1.

14:33 Then 2 again.

14:34 1 divided by 2.

14:36 Giving you 0.

14:37 Remember 1.

14:39 So, answer for 7 in base 10.

14:43 The equivalent in base 2 is, remember, draw your arrow.

14:47 You're writing from the bottom to the top.

14:49 So, you have 1, 1, 1 to number in base 2.

14:54 So, that's the answer.

14:58 You can see that we both, we are answers for the subtraction method.

15:05 And that for the successive division method are the same.

15:09 So, when you have to convert numbers to base 10 to base 2.

15:12 Any which one you feel convenient for you, you're free to use.

15:16 So, I have exercises using any convenient method.

15:19 Convert the numbers and the table below to base 2 numbers.

15:26 So, yeah, numbers in base 10, 1 to 10, 11 to 20.

15:30 So, using any of this method, convert these numbers, which are in base 10 to numbers in base 2.

15:39 Thank you for watching.

15:41 I am Esther Oluci-Ibebrike, till we meet next time.