Numbers In Base Two

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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

1. 1110 + 1001 2.         1111 + 1101 + 101

Solutions:

$$\begin{gathered} 1. 1110 \\ +\frac{1001}{{\displaystyle \frac{10111}{}}} \end{gathered}$$

 

$$\begin{gathered} 2. 1111 \\ 1101 \\ + \frac{101}{{\displaystyle \frac{100001}{}}} \end{gathered}$$

 

Note: 11 take 1 carry 1

10 take 0 carry 1

100 take 0 carry 10

 

 

EVALUATION

1. Simplify the following 101 + 101 +111
2. 10101 + 111

 

 

ADDITION IN BICIMALS

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

 

Example:

1. 1.1011_two +   10.1001_two  +  10.01
2. 10.001_two+ 101.111

 

Solution:

 

$$\begin{gathered} 1) 1.1011 \\ 10.1001 \\ + \frac{10.0100}{{\displaystyle \frac{110.{1000}_{two}}{}}} \\ 2) 101.111 \\ +\frac{10.001}{{\displaystyle \frac{1000.000}{}}} \end{gathered}$$]

 

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:

$$\begin{gathered} \left(a\right) 1110 \\ – \frac{1001}{{\displaystyle \frac{101}{}}} \end{gathered}$$

 

SUBTRACTION IN BICIMAL

Example

101.101_two – 11.011_two

$$\begin{gathered} solution: \\ 101.101 \\ \frac{11.011}{{{\displaystyle \frac{10.010}{}}}_{}} \end{gathered}$$

 

EVALUATION

1. 10111÷110
2. 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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