Numbers with base value 2 are known as binary numbers. They are represented using two digits i.e. 0 and 1. For example: 01011 represents (0 × 24) + (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20), they represent 0 + 8 + 0 + 2 + 1, and equals to 11. Now we will see how we will represent the digits in binary notation.
Decimal Number |
Binary Number |
0 |
0000 |
1 |
0001 |
2 |
0010 |
3 |
0011 |
4 |
0100 |
5 |
0101 |
6 |
0110 |
7 |
0111 |
8 |
1000 |
9 |
1001 |
10 (A) |
1010 |
11 (B) |
1011 |
12 (C) |
1100 |
13 (D) |
1101 |
14 (E) |
1110 |
15 (F) |
1111 |
16 (10) |
10000 |
Now we will see how to convert a number represented using Binary Number System to decimal number. Suppose we have 100101 which is in binary form. As we discussed above binary number is always written in 0 and 1 form. So we can convert it into decimal form as:
0 + 0 |
0 |
0 + 1 |
1 |
1 + 0 |
1 |
1 + 1 |
0 |
Using these conditions we can add binary numbers.