How it works
Octal counts in base 8, binary counts in base 2. Converting means rewriting the same quantity with a different set of digits — the value never changes, only how it is written.
- Convert each octal digit to its decimal value and add them up.
- Divide that total by 2, keeping the remainders.
- Read the remainders bottom to top for the binary result.
The reverse conversion is Number Converter, which also handles every other base pair.
Examples
Worked examples, digit by digit:
- 12 (octal) = 10 in decimal = 1010 (binary)
- 25 (octal) = 21 in decimal = 10101 (binary)
- 377 (octal) = 255 in decimal = 11111111 (binary)
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 4 | 100 | 4 | 4 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 100 | 1100100 | 144 | 64 |
| 255 | 11111111 | 377 | FF |
Octal to Binary: frequently asked questions
- How do I convert octal to binary?
- Replace each octal digit with its 3-bit binary equivalent. For example, octal 55 is 101101 in binary. The converter above does this instantly for any value.
- What is 377 in binary?
- Octal 377 equals 11111111 in binary (the value 255, the largest number that fits in one byte).
- Why are octal and binary used?
- Octal (base 8) is a compact way to write groups of three bits and is still used for Unix file permissions such as 755. Binary (base 2) is how computers store data, as bits that are either 0 or 1.