Convert binary to octal
1011 in binary is 13 in octal. 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
1011 in binary
13
How it gets there
- Each digit carries its place
- 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰
- Which is
- 8 + 0 + 2 + 1 = 11
- Divide by 8, keeping the remainders
- 11 ÷ 8 = 1 remainder 3 1 ÷ 8 = 0 remainder 1
- Read the remainders upwards
- The last remainder is the leading digit.
binary to octal, at a glance
One octal digit is exactly three binary digits, so this conversion is done by grouping rather than by dividing: split the binary into threes from the right and read each group. It is why Unix file permissions are written in octal — three bits, read-write-execute, per group.
| binary | octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 10 |
| 1001 | 11 |
| 1010 | 12 |
| 1011 | 13 |
| 1100 | 14 |
| 1101 | 15 |
| 1110 | 16 |
| 1111 | 17 |
| 10000 | 20 |
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.