Octal to binary converter
Type an octal number with digits 0 to 7 to get its binary value. Each octal digit becomes exactly 3 bits, so 377 becomes 11111111. Paste a list to convert many numbers at once.
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How to convert octal to binary
- Take each octal digit on its own.
- Write it as 3 bits, keeping leading zeros: 5 is 101, 2 is 010, 0 is 000.
- Join the groups in the same order.
- Drop any zeros at the far left if you want the short form.
The Output menu can pad the result to 8 bits, split it into groups of 4 or 8, or add a 0b prefix for code. Hex converts the same way with 4 bits per digit in hex to binary.
Octal to binary table
| Octal | Binary | Octal | Binary |
|---|---|---|---|
| 0 | 000 | 4 | 100 |
| 1 | 001 | 5 | 101 |
| 2 | 010 | 6 | 110 |
| 3 | 011 | 7 | 111 |
The digits 8 and 9 do not exist in octal. If you type one, the tool points to it, because the number is probably decimal.
Worked examples
| Octal | Each digit as 3 bits | Binary |
|---|---|---|
| 12 | 001 010 | 1010 |
| 56 | 101 110 | 101110 |
| 377 | 011 111 111 | 11111111 |
| 644 | 110 100 100 | 110100100 |
| 1000 | 001 000 000 000 | 1000000000 |
For 377: 3 is 011, 7 is 111 and 7 is 111. Joined that is 011111111, and without the leading zero it is 11111111, which is 255 in decimal, as the binary to decimal converter shows.
Reading Unix permissions in binary
Each digit in a chmod value is 3 bits: read (4), write (2) and execute (1), the same values the chmod manual page uses. Converting to binary shows which ones are on. To turn a bit pattern such as 111 101 101 back into a chmod value, use binary to octal.
| Octal | Binary | Letters | Typical use |
|---|---|---|---|
| 755 | 111 101 101 | rwxr-xr-x | Programs and folders |
| 644 | 110 100 100 | rw-r--r-- | Normal files |
| 600 | 110 000 000 | rw------- | Private keys |
| 777 | 111 111 111 | rwxrwxrwx | Everyone can do everything (avoid) |
Frequently asked questions
How many bits is one octal digit?
Three. That is why octal converts to binary digit by digit.
What is 7 in binary?
111. It is the largest octal digit and uses all three bits.
Why does 377 give 8 bits and not 9?
Three digits make 011111111, but the leading 0 adds nothing to the value, so the tool drops it. Pick Pad to 8 bits or a group option in Output to keep a fixed width.
Can I convert octal fractions?
Yes. Type a point, such as 0.54, and each digit after it becomes 3 bits too. 0.54 is 0.1011 in binary.