Binary Number System:
As stated before, binary numbers are depicted using 0s and 1s. Any 4-digit binary number ABCD may be converted into its decimal equivalent as follows:
A × 23 + B × 22 + C × 21 + D × 20 where Boolean variables A, B, C and D can take values either 0 or 1. For example, 1100 and its decimal equivalent value is 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20 = 12. For reference, first 16 binary numbers and their decimal equivalents are illustrated in Table
Table: First 16 Binary Numbers and their Decimal Values
|
Binary Numbers
|
Decimal Values
|
|
0 0 0 0
|
0
|
|
0 0 0 1
|
1
|
|
0 0 1 0
|
2
|
|
0 0 1 1
|
3
|
|
0 1 0 0
|
4
|
|
0 1 0 1
|
5
|
|
0 1 1 0
|
6
|
|
0 1 1 1
|
7
|
|
1 0 0 0
|
8
|
|
1 0 0 1
|
9
|
|
1 0 1 0
|
10
|
|
1 0 1 1
|
11
|
|
1 1 0 0
|
12
|
|
1 1 0 1
|
13
|
|
1 1 1 0
|
14
|
|
1 1 1 1
|
15
|