How to use the binary to octal converter
- 1Type the bits into Binary (base 2).
- 2Read the result in Octal (base 8); decimal and hex appear under Other bases.
- 3Open Step-by-step working to see each group of three bits and its octal digit.
- 4Press Swap to convert octal back to binary, or Copy to copy a result.
Example
111101101
Octal: 755 Decimal: 493 Hexadecimal: 1ED
111 = 7, 101 = 5, 101 = 5. These are the rwxr-xr-x permission bits.
Grouping bits in threes
Eight is 2³, so one octal digit equals three bits. Split the binary number into threes from the right, pad the leftmost group with zeros, and replace each group with its digit:
1101011 → 001 101 011 → 153.
Fractions work the same way after the point, but grouped from the left and padded on the right: 0.11 → 0.110 → 0.6.
Binary-octal table
| Octal | Binary | Octal | Binary |
|---|---|---|---|
| 0 | 000 | 4 | 100 |
| 1 | 001 | 5 | 101 |
| 2 | 010 | 6 | 110 |
| 3 | 011 | 7 | 111 |
Octal and Unix file permissions
Unix permissions are nine bits: read, write and execute for the owner, the group and everyone else. Grouping them in threes is exactly an octal conversion, which is why chmod takes octal numbers:
| Bits | rwx | Octal |
|---|---|---|
| 111 101 101 | rwx r-x r-x | 755 |
| 110 100 100 | rw- r-- r-- | 644 |
| 111 000 000 | rwx --- --- | 700 |
Each position is read = 4, write = 2, execute = 1.
Checking your answer via decimal
To check an octal result, convert both numbers to decimal. 755₈ is 7 × 64 + 5 × 8 + 5 = 493, and 111101101₂ is 256 + 128 + 64 + 32 + 8 + 4 + 1 = 493. The decimal field under Other bases shows this value as you type, and binary to decimal shows the full working.
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