Back to: MATHEMATICS JSS3

**Welcome to Class !!**

*We are eager to have you join us !!*

*In today’s Mathematics class, We will be looking at Multiplication and Division in Base Two. We hope you enjoy the class!*

**MULTIPLICATION AND DIVISION IN BASE TWO**

In multiplication, 0 x 0 = 0, 1 x 0 = 0, 1 x 1 = 1.

When there is long multiplication of binary numbers, the principle of addition can be used to derive the answer. Under division, the principle of subtraction can be used.

**Worked Examples:**

- 1110 x 111

Solution:

$1)1110\phantom{\rule{0ex}{0ex}}\times \frac{110}{0000}\phantom{\rule{0ex}{0ex}}1110\phantom{\rule{0ex}{0ex}}\frac{1110}{1010100}$

- Multiply 11.01 by 1.1 in base two

**Solution:**

$1101\phantom{\rule{0ex}{0ex}}\frac{x11}{1101}\phantom{\rule{0ex}{0ex}}\frac{1101}{100.111}$

**DIVISION IN BASE TWO**

Example:

Divide 110010101 by 1111

Solution:

110010101_{2} ÷ 1111_{2} = 11011_{2}

**Example:**

Find the square root of 1010001_{2}

Solution:

First convert it to base 10

10100012 = 1 x 2 ^{6}+ 0 + 1 x 2 ^{4}+ 0 + 0 + 0 + 1 x 2^{0}

= 64 + 16 + 1 = 81_{ten}

The square root of 81 = 9_{ten}

2 | 9 1

2 | 4 0

2 | 2 0

2 | 1 1

0 | 0

= 1001_{2}

**EVALUATION**

- 10111÷110
- 10001 x 11

*We have come to the end of this class. We do hope you enjoyed the class?*

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*In our next class, we will be talking about Rational and Non-Rational Numbers Variation. We are very much eager to meet you there.*

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