00:11 Hello everyone, I am your Mathematics teacher, Esther Oluchi Ibebukwe.

00:18 Today, our topic is counting in base two.

00:23 By the end of this lesson, you should be able to count in group of two's.

00:28 Number basis, a number base is the number of digit or combination of digit

00:34 that is system of counting users to represent numbers.

00:38 A base can be a own number greater than zero.

00:42 Some people traditionally counting fives or the count in 20.

00:47 When counting in days of the week, we count in sevens.

00:51 But when counting is second in a minute, we count in sisters.

00:55 However, for most purposes, people count in base 10,

00:59 which is known as a decimal system.

01:02 We have digit zero, one, two, three, four, five, six, seven, eight, and nine.

01:08 We use this digit to represent numbers in base 10.

01:12 The binary system is the second in importance to our usual base 10 system.

01:17 It is important because it is using computer programs.

01:21 Binary numbers are made up of two digits, which is zero and one.

01:25 A computer contains a large number of switches.

01:29 Each switch is either off or on.

01:33 An off switch represents one, an off switch represents zero.

01:38 Base 8 and 16 are also popular because of its use in modern technology.

01:45 Now, counting in groups of two.

01:48 Counting in group of two is also known as a binary base system.

01:52 A binary number is made up of zero and one, like I said earlier.

01:56 An example is one, zero, one, one in base two.

02:01 One, zero, one, one in base two.

02:06 The figure shows the place value of digits in the binary number.

02:11 We have two rest of four of three, two rest of four of two, two rest of four of one.

02:17 You can also show these by using counters on the paper abacost as shown below.

02:23 We have a paper abacost.

02:26 For example, we can have...

02:33 We use this paper abacost to improvise.

02:36 I don't know if you've seen an abacost in real life.

02:41 We have 8, fours, twos, then units.

02:54 Okay, then we have one here, nothing here, one here, one here.

03:12 I would like us to do this together, I would like you to pay close attention.

03:15 Make a paper abacost as in the figure above.

03:19 A paper abacost you can draw this on your paper.

03:22 If you don't have an abacost available with you,

03:25 you can improvise by drawing this in our notebook.

03:28 We have 8, 4, 2, and units.

03:32 So when you make this on your paper, we count out nine counters.

03:37 Our counters can be maybe a cock of a bottle.

03:41 It could be a stick of matches.

03:43 So whatever it is that you can use to count, can serve as a counter.

03:47 So let's have them.

03:48 The activities are online on the slide.

03:49 We have count out nine counters.

03:52 Group them in twos.

03:54 Now group the peers in 8, 4, 2, and 9 as far as possible.

03:59 Then represent the binary number for 9 on your paper abacost.

04:04 Now let's have our counters.

04:06 For example, let me use stick like maybe a stick.

04:09 Let's count out nine.

04:11 I want to do this together.

04:12 You can do that on your own end.

04:13 Three, four, five, six, seven, eight, nine.

04:25 These are nine counters.

04:26 Now we have to group them in twos.

04:29 We want to group this nine.

04:31 We want to group them in twos.

04:33 In group them in twos, we can have, let me do this.

04:38 One, two, one, one, two, I have two.

04:42 One, two, I have three.

04:45 One, two, I have four.

04:47 I have one left.

04:49 That's me grouping them in twos.

04:50 I'm going to have in twos into four places.

04:52 One, two, three, then four.

04:59 Then I have one left.

05:01 Okay, let's continue the activity.

05:03 Then next one now is to group them in eight,

05:10 four, two, and units.

05:12 Okay, let's see, let's do that now.

05:14 We've grouped this into, now let's group it to eight.

05:19 One, two, three, four, five, six, seven, eight.

05:21 That means if you group this into eight,

05:23 all of this will give us one group of eight.

05:27 Now we'll have to do one.

05:28 So we have one, two, three, four, five, six, seven, eight.

05:36 So this is eight.

05:37 Then we have one standing alone.

05:40 So what next are we asked to do?

05:42 So we asked to represent this on a paper abacus.

05:46 So on a paper abacus, let's draw abacus.

05:50 A paper abacus.

05:51 Let's draw a paper abacus.

05:58 Um, we have eight, eight, we have fours, then we have twos, then we have ones.

06:06 So from here now, these are nine sticks,

06:09 which are present nine in base ten.

06:12 Then we want to convert this nine now to a number in base two.

06:17 So what do we do?

06:18 And we are told to group them into eight and one.

06:21 We've done that into two.

06:22 Now we have a group of these eight and many times one.

06:26 So we write one in four.

06:28 We don't have any four.

06:28 We already have eight.

06:29 We don't have four.

06:30 So we leave this space open or put zero.

06:33 Then in two, we don't have two.

06:35 We have zero.

06:36 Then we have one.

06:38 We have one.

06:39 So okay, let's see what we have here.

06:43 We can see that this we have four nine, which is in base ten.

06:51 The equivalent in the binary number is one.

06:55 Zero, zero, one in base two.

06:59 We have grouped nine into twos and have it as one, zero, zero, one.

07:08 Now we have xR exercise for you.

07:12 Use the method in example one to represent

07:14 the numbers from one to twenty in base two in a paper abacus.

07:20 So for each number, you're going to do this.

07:23 Group them into eight, four, two, and one.

07:27 We have done number nine for you, which is number nine in base ten.

07:30 These are numbers in base ten and you ask to convert them to numbers in base two.

07:35 So we have done the number nine in base ten, which is equal to one, zero, zero,

07:39 one in base two.

07:41 So the assignment right here now is for you to do for number one to the other

07:46 nineteen numbers, which is between one and eight to the number ten and eleven and twenty.

07:52 So before I go, let me solve one more example.

07:55 Let me speak number ten in base ten.

07:59 Let me convert it to base two for better understanding.

08:03 So let's go.

08:05 We have ten in base ten.

08:08 So let's represent the powers of two on our paper abacus.

08:14 So we have

08:19 we have the eights, fours, twos, then units, which is once.

08:25 So now let's start.

08:27 Let's group them.

08:29 Let's group the number ten in eight, four, two, and one.

08:37 So let's count our count us, our eight count us, our ten count us rather.

08:43 We have one, two, three, four, five, six, seven, eight, nine, ten.

08:51 So let's group into eight, one, two, three, four, five, six, seven, eight.

08:58 So this is, this is our eights count us.

09:00 So we have those two lefts.

09:03 So having two left, we have a group of eights, then two lefts.

09:10 Now from here, now we can see that we have eights.

09:12 So remember I said earlier that the number, the binary numbers,

09:16 are only two digits, which are zero and one.

09:19 So once there's something you write one, I mean there's nothing you write zero.

09:24 So there's only like three, four, five, six, in binary numbers.

09:28 So for this now, we have eight.

09:31 So I write one here.

09:32 For four, we don't have a four, we don't have a four here.

09:35 So I can leave it as nothing or I write zero.

09:39 So yeah, there's nothing here too.

09:41 Okay, yes, two, we have two.

09:43 So I write one for two.

09:44 So this two is now gone.

09:46 We don't have nothing left.

09:47 So nothing here.

09:48 So for our base, for our ten,

09:50 the equivalent in base two is one, zero, one, zero in base two.

10:01 So with this now, you'll be able to solve the rest.

10:05 Thank you for watching.

10:07 I am Ibibi K. Esther Olucci.

10:11 See you in the next time.