Thursday, February 28, 2013

Binary Conversion

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

Answer: 7110= 10001112

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

Answer: 11011012 = 10910