What is Binary?
Binary is the language of computers that uses only two digits 0 and 1.
What is Decimal?
Decimal is our everyday numbers. It uses ten digits 0 to 9.
How to Convert Binary to Decimal
Each digit in a binary number stands for a power of 2. From right to left, the powers are 2^0, 2^1, 2^2, 2^3, and so on.
Small Example: Convert 1011 to Decimal
- Write out the binary number: 1011
- List the powers of 2:
- Rightmost 1: 2^0 = 1
- Second 1: 2^1 = 2
- 0: 2^2 = 4 (but we ignore this because the digit is 0)
- Leftmost 1: 2^3 = 8
- Add up the values where there's a 1: 8 + 2 + 1 = 11
So, 1011 in binary equals 11 in decimal.
Another Example: 10110
10110 = 16 + 0 + 4 + 2 + 0 = 22 in decimal
Conversion Table
| Binary | Decimal | Explanation |
|---|---|---|
| 0000 | 0 | No bits set |
| 0001 | 1 | 2^0 = 1 |
| 0010 | 2 | 2^1 = 2 |
| 0011 | 3 | 2^1 + 2^0 = 2 + 1 |
| 0100 | 4 | 2^2 = 4 |
| 0101 | 5 | 2^2 + 2^0 = 4 + 1 |
| 0110 | 6 | 2^2 + 2^1 = 4 + 2 |
| 0111 | 7 | 2^2 + 2^1 + 2^0 = 4 + 2 + 1 |
| 1000 | 8 | 2^3 = 8 |
| 1001 | 9 | 2^3 + 2^0 = 8 + 1 |
| 1010 | 10 | 2^3 + 2^1 = 8 + 2 |
| 1011 | 11 | 2^3 + 2^1 + 2^0 = 8 + 2 + 1 |
| 1100 | 12 | 2^3 + 2^2 = 8 + 4 |
| 1101 | 13 | 2^3 + 2^2 + 2^0 = 8 + 4 + 1 |
| 1110 | 14 | 2^3 + 2^2 + 2^1 = 8 + 4 + 2 |
| 1111 | 15 | 2^3 + 2^2 + 2^1 + 2^0 = 8 + 4 + 2 + 1 |