Back to: MATHEMATICS JSS3

**Welcome to Class !!**

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

*In today’s Mathematics class, We will be discussing Numbers in Base 2. We hope you enjoy the class!*

**BINARY NUMBERS (BASE 2 NUMBERS)**

- Addition in base 2
- Subtraction in base 2
- Multiplication & Division in base 2

** **

**ADDITION IN BASE TWO**

We can add binary numbers in the same way as we separate with ordinary base 10 numbers.

The identities to remember are:-

0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10, 1 + 1 + 1 = 11, 1 + 1 + 1 + 1 = 100

**Worked Examples**

Simplify the following

- 1110 + 1001 2. 1111 + 1101 + 101

Solutions:

$1.1110\phantom{\rule{0ex}{0ex}}+\frac{1001}{{\displaystyle \frac{10111}{}}}\phantom{\rule{0ex}{0ex}}$

$2.1111\phantom{\rule{0ex}{0ex}}1101\phantom{\rule{0ex}{0ex}}+\frac{101}{{\displaystyle \frac{100001}{}}}\phantom{\rule{0ex}{0ex}}$

Note: 11 take 1 carry 1

10 take 0 carry 1

100 take 0 carry 10

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**EVALUATION**

- Simplify the following 101 + 101 +111
- 10101 + 111

**ADDITION IN BICIMALS**

In bicimals, the binary point is placed underneath each other exactly the same way like ordinary decimals.

Example:

- 1.1011
_{two}+ 10.1001_{two}+ 10.01 - 10.001
_{two}+ 101.111

Solution:

$1)1.1011\phantom{\rule{0ex}{0ex}}10.1001\phantom{\rule{0ex}{0ex}}+\frac{10.0100}{{\displaystyle \frac{110.{1000}_{two}}{}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}2)101.111\phantom{\rule{0ex}{0ex}}+\frac{10.001}{{\displaystyle \frac{1000.000}{}}}$]

**SUBTRACTION IN BASE TWO**

The identities to remember on subtraction are: 0 – 0 = 0, 1 – 0 = 1, 10 – 1 = 1, 11 – 1 = 10, 100 – 1 = 11

Worked Examples

Simplify the following:-

(a) 1110 – 1001

**Solutions:**

$\left(a\right)1110\phantom{\rule{0ex}{0ex}}\u2013\frac{1001}{{\displaystyle \frac{101}{}}}$

**SUBTRACTION IN BICIMAL**

Example

101.101_{two} – 11.011_{two}

$solution:\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}101.101\phantom{\rule{0ex}{0ex}}\frac{11.011}{{{\displaystyle \frac{10.010}{}}}_{}}$

**EVALUATION**

- 10111÷110
- 10001 x 11

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

*Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.*

*In our next class, we will be talking about Numbers in Base II. We are very much eager to meet you there.*

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