Converting binary to decimal
Given the binary value 1000:
1000
= 1 * 23 + 0 * 2² + 0 * 21 + 0 * 20
= 23
= 8 (decimal)
Converting decimal to binary
Given the decimal value 10:
10
= 23 + 21
= 1 * 23 + 0 * 22 + 1 * 21 + 0 * 20
= 1010 (binary)
An easier way to work this out is, for example, given a decimal number of 11:
- divide the decimal number by 2, recording the quotient and remainder in the next row
- rounding the quotient DOWN each time, until you have a quotient of 0.
| Quotient | Remainder | ||
|---|---|---|---|
| 11 | |||
| Repeat the procedure - divide by 2, record quotient and remainder in the next row | 5 | 1 | 11/2 = 5 remainder 1 |
| Repeat again | 2 | 1 | 5/2 = 2 remainder 1 |
| Repeat again | 1 | 0 | 2/2 = 1 remainder 0 |
| Stop! Quotient = zero | 0 | 1 | 1/2 = 0 remainder 1 |
Result: (read from bottom up) Decimal value 11 = binary 1011