Convert decimal to binary
255 in decimal is 11111111 in binary. Each digit is multiplied by its place value — the base raised to the digit's position, counting from zero on the right — and the products are added. The page prints every one of those products rather than only the total. The conversion is exact: bases are positional notation for the same number, so nothing is rounded and the result can be checked digit by digit.
Conversion rules checked · How we check
255 in decimal
11111111
How it gets there
- Divide by 2, keeping the remainders
- 255 ÷ 2 = 127 remainder 1 127 ÷ 2 = 63 remainder 1 63 ÷ 2 = 31 remainder 1 31 ÷ 2 = 15 remainder 1 15 ÷ 2 = 7 remainder 1 7 ÷ 2 = 3 remainder 1 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1
- Read the remainders upwards
- The last remainder is the leading digit.
decimal to binary, at a glance
The conversion every other one is defined against. Each binary place is a power of two, so the value is a sum: 1011 is 8 + 0 + 2 + 1. Going back is repeated division by two, reading the remainders upwards.
| decimal | binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
Why is the working shown?
Every other converter of this kind prints the answer and stops. A base is a positional system, so the answer is a sum you can check: each digit is multiplied by the base raised to its position, and the results are added. Going the other way is repeated division, reading the remainders upwards. Neither is a black box, and this page refuses to be one.