# How to convert decimal numbers to binary and binary by tlv10296

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```									How to convert decimal numbers to binary and binary to decimal

Integers:
Decimal to Binary:
For example: 12

12               2

12
6      2
0
6
3          2
0       2
1
1

1100

12 (Decimal) = 1100 (Binary)

Binary To Decimal:
For Example 10011

1 * 20   =1
1 * 21   =2 +
0 * 22   =0 +
0 * 23   =0 +
1 * 24   = 16 +
= 19

10011 (Binary) = 19 (Decimal)
Fractions:
Decimal To Binary:
For Example: 0.6

0.6 = a1 * 2-1 + a2 * 2-2 + ….. + an * 2-n
*2
1.2 = a1 + a2 * 2-1 + ….. + an * 2-n+1           a1 = 1
0.2 = a2 * 2-1 + a3 * 2-2 + ….. + an * 2-n+1
*2
0.4 = a2 + a3 * 2-1 + a4 * 2-2….. + an * 2-n+2   a2 = 0
0.4 = a3 * 2-1 + a4 * 2-2….. + an * 2-n+1
*2
0.8 = a3 + a4 * 2-1 + a5 * 2-2….. + an * 2-n+3   a3 = 0
0.8 = a4 * 2-1 + a5 * 2-2….. + an * 2-n+3
*2
1.6 = a4 + a5 * 2-1 + a6 * 2-2….. + an * 2-n+4   a4 = 1
0.6 = a5 * 2-1 + a6 * 2-2….. + an * 2-n+4
Return to first step

0.6 (Decimal) = 0.100110011001100110011001100…………
0.6(decimal )  0.1001100 ( Binary )

Binary to Decimal
For Example: 0.11001

0.11001
1 * 2-1   = 1/2
1 * 2-2   = 1/4
0 * 2-3   =0
0 * 2-4   =0
1 * 2-5   = 1/32

(16  8  1) / 32  25 / 32 = 0.78125

```
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