Octal to Binary Converter
Convert octal numbers to binary format
Tip: Enter an octal number (0-7 only). The conversion happens in real-time.
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Octal to binary, step by step
Convert octal to binary
Type an octal number, with or without 0o in front, and its binary form appears as you type. Results longer than four digits are also split into groups of four bits, and the window bar shows the bit length.
Each octal digit is exactly three bits, so the conversion is a lookup rather than arithmetic: swap every digit for its three bits and join them. The digits 8 and 9 do not exist in octal, and typing one shows an error instead of a guess.
How to convert octal to binary by hand
Replace each octal digit by its three bits, from 0 = 000 to 7 = 111, and join the groups. For 2675:
| Octal digit | Three bits |
|---|---|
| 2 | 010 |
| 6 | 110 |
| 7 | 111 |
| 5 | 101 |
Joined, that is 010 110 111 101. Without the leading zero, 2675 in octal is 10110111101 in binary. The step-by-step window above lists the three bits of every digit you type.
File permissions in binary
| Octal | Binary | Permission |
|---|---|---|
| 400 | 100000000 | r-------- |
| 444 | 100100100 | r--r--r-- |
| 600 | 110000000 | rw------- |
| 644 | 110100100 | rw-r--r-- |
| 664 | 110110100 | rw-rw-r-- |
| 700 | 111000000 | rwx------ |
| 750 | 111101000 | rwxr-x--- |
| 755 | 111101101 | rwxr-xr-x |
| 775 | 111111101 | rwxrwxr-x |
| 777 | 111111111 | rwxrwxrwx |
Read the binary in threes and every 1 is a letter: 110 100 100 is rw- r-- r--, the usual setting for a file, and 111 101 101 is rwx r-x r-x, the usual setting for a folder or a script.
Have the bits already?
The binary to octal converter splits bits into groups of three and writes each as an octal digit.
For the decimal value of an octal number, use the octal to decimal converter; the number system converter shows all four bases at once.
Octal to binary questions
11111111. 3 is 011 and each 7 is 111; without the leading zero that is eight ones.
8 is 2 to the power 3, so three bits give exactly eight patterns, 000 to 111, one for each digit from 0 to 7.
Yes. A leading zero does not change the value, so 0755 and 755 both give 111101101.
No. The shortest binary form is shown, so 7 gives 111 and 10 gives 1000. Add zeros on the left if you need a fixed width.
No. The conversion runs in your browser.