# Binary Conversion

## Binary Conversion

 Power, p 2P 0 1 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512

Fig 2 Some powers of 2

## CONVERSION OF DECIMAL INTEGERS TO BINARY Method

1- Write out powers of 2 in a line starting at the right with 1. That is write ... 64 32 16 8 4 2 1 (as many as necessary).

2- Subtract these powers of 2 from the number. Each time subtract the largest one which will go.

3- When a power is subtracted write a 1 under that power, otherwise write a 0.

## Worked question

Convert the decimal number 71 to binary.

64 32 16 8 4 2 1 (The line of powers)

1 0 0 0 1 1 1 (The Is and Os written down while subtracting)

71-

64

7-

4

3-

2

CONVERSION OF BINARY INTEGERS TO DECIMAL

## Method

1- Write powers of 2 above the digits of the binary numbers. Start at the right-hand end. That is write ... 64 32 16 8 4 2 1 (as many as necessary).

2- Write down the powers of 2 which are above a 1 in the binary number. Add them up to obtain the answer.

## Worked question

Convert the binary number 1101101 to decimal.

64 32 16 8 4 2 1

1 1 0 1 1 0 1

Number = 64+32+8+4+ 1

=109