Octal to Binary Converter
Type an octal number and this octal to binary converter writes each digit as 3 bits: 755 becomes 111 101 101. Octal has no 8 or 9, so the converter points those out.
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Octal to binary
Binary
How to convert octal to binary
- 01
Take each digit
Work through the octal number one digit at a time, left to right.
- 02
Write it as 3 bits
Use the chart below: 7 is
111, 5 is101, 0 is000. Keep the zeros inside the number. - 03
Join the groups
Put the groups side by side. Zeros at the very start can go: octal 17 is
001 111, or1111.
Octal to binary chart
| Octal | Binary | Decimal |
|---|---|---|
| 0 | 000 | 0 |
| 1 | 001 | 1 |
| 2 | 010 | 2 |
| 3 | 011 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
Where octal is used
Octal shows up wherever bits come in threes. The best known place is file permissions on Linux and macOS: each digit of chmod 755 is one 3-bit group of read, write and execute flags, so 7 is 111 (all three) and 5 is 101 (read and execute).
Older computers with 12, 24 or 36-bit words used octal too, because those widths split evenly into groups of 3. Today hex is more common, since a byte splits evenly into two groups of 4.
Frequently asked questions
How do you convert octal to binary?
Replace each octal digit with its 3-bit value and keep the order. Octal 52 is 101 010: 5 is 101 and 2 is 010.
What is 7 in binary?
7 is 111 in binary. It is 4 + 2 + 1, every place of a 3-bit group switched on, and the same digit in octal and decimal.
What is octal used for?
Mostly file permissions on Linux and macOS, such as chmod 644, where each digit packs 3 permission bits. Some programming languages also read a number with a leading 0 or 0o as octal.