How to use the octal to binary converter
- 1Type the octal number into Octal (base 8). Only digits 0–7 are allowed; a
0oprefix is fine. - 2Read the bits in Binary (base 2). Tick Keep leading zeros for exactly three bits per digit.
- 3See the digit-by-digit lookup under Step-by-step working, then press Copy.
Example
644
Binary: 110100100 Decimal: 420 Hexadecimal: 1A4
6 = 110 (rw-), 4 = 100 (r--), 4 = 100 (r--).
Each octal digit is three bits
Write each digit as three bits and join them. 755 → 111 101 101 = 111101101. Because 8 = 2³, the groups are independent; there is nothing to carry. Drop leading zeros from the first group if you want the shortest form (octal 3 is 11, not 011), or tick Keep leading zeros to keep the full width.
Octal-binary table
| Octal | Binary | Octal | Binary |
|---|---|---|---|
| 0 | 000 | 4 | 100 |
| 1 | 001 | 5 | 101 |
| 2 | 010 | 6 | 110 |
| 3 | 011 | 7 | 111 |
Reading chmod values in binary
In a permission such as 755, each digit is one class of user (owner, group, others), and each of its three bits is one permission: read (4), write (2), execute (1).
| Octal | Binary | Meaning |
|---|---|---|
| 7 | 111 | read, write, execute |
| 6 | 110 | read, write |
| 5 | 101 | read, execute |
| 4 | 100 | read only |
| 0 | 000 | no access |
So 644 = 110 100 100 = rw-r--r--, the usual setting for web files, and 755 = rwxr-xr-x for folders and scripts.
Octal to decimal and hex
The other fields update at the same time. Octal 755 is 493 in decimal (7 × 64 + 5 × 8 + 5) and 1ED in hex. To go from octal to hex by hand, convert to binary first and regroup the bits in fours: 1 1110 1101 = 1ED. The hex to binary converter does the reverse grouping.
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