What is Decimal?
Decimal is our everyday number system. It uses ten digits: 0 to 9.
What is Binary?
Binary is a number system that uses only two digits 0 and 1. Computers use binary to process data.
How to Convert Decimal to Binary
To change a decimal number to binary:
- Divide the number by 2
- Keep track of the remainder (0 or 1)
- Divide the result by 2 again
- Repeat until you get 0
- Read the remainders from bottom to top
Step by Step Example How to Convert 13 to Binary
| Division | Result | Remainder |
|---|---|---|
| 13 ÷ 2 = 6 | 6 | 1 |
| 6 ÷ 2 = 3 | 3 | 0 |
| 3 ÷ 2 = 1 | 1 | 1 |
| 1 ÷ 2 = 0 | 0 | 1 |
Reading the remainders from bottom to top: 13 in decimal = 1101 in binary
Conversion Table
| Decimal | Binary | Explanation |
|---|---|---|
| 0 | 0000 | Zero in both systems |
| 1 | 0001 | Smallest positive number |
| 2 | 0010 | 2^1 |
| 3 | 0011 | 2^1 + 2^0 |
| 4 | 0100 | 2^2 |
| 5 | 0101 | 2^2 + 2^0 |
| 6 | 0110 | 2^2 + 2^1 |
| 7 | 0111 | 2^2 + 2^1 + 2^0 |
| 8 | 1000 | 2^3 |
| 9 | 1001 | 2^3 + 2^0 |
| 10 | 1010 | 2^3 + 2^1 |
| 11 | 1011 | 2^3 + 2^1 + 2^0 |
| 12 | 1100 | 2^3 + 2^2 |
| 13 | 1101 | 2^3 + 2^2 + 2^0 |
| 14 | 1110 | 2^3 + 2^2 + 2^1 |
| 15 | 1111 | 2^3 + 2^2 + 2^1 + 2^0 |