How to convert octal to binary by hand
Example 1: 755 in octal is 111101101 in binary
Octal to binary: write each digit as 3 bits
Because 8 = 2³, every octal digit maps to exactly 3 binary digits. Drop any leading zeros at the end.
| Octal digit | Value | 3 bits |
|---|---|---|
| 7 | 7 | 111 |
| 5 | 5 | 101 |
| 5 | 5 | 101 |
111 101 101 → 111101101
Example 2: 640 in octal is 110100000 in binary
Octal to binary: write each digit as 3 bits
Because 8 = 2³, every octal digit maps to exactly 3 binary digits. Drop any leading zeros at the end.
| Octal digit | Value | 3 bits |
|---|---|---|
| 6 | 6 | 110 |
| 4 | 4 | 100 |
| 0 | 0 | 000 |
110 100 000 → 110100000
Octal to Binary conversion table
| Octal | Binary | Decimal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 3 | 11 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
| 10 | 1000 | 8 |
| 11 | 1001 | 9 |
| 12 | 1010 | 10 |
| 13 | 1011 | 11 |
| 14 | 1100 | 12 |
| 15 | 1101 | 13 |
| 16 | 1110 | 14 |
| 17 | 1111 | 15 |
| 20 | 10000 | 16 |
| 40 | 100000 | 32 |
| 100 | 1000000 | 64 |
| 144 | 1100100 | 100 |
| 200 | 10000000 | 128 |
| 377 | 11111111 | 255 |
| 400 | 100000000 | 256 |
| 1000 | 1000000000 | 512 |
| 1750 | 1111101000 | 1000 |
| 2000 | 10000000000 | 1024 |
Where this conversion comes up
- Reading chmod values as permission bits: 7 is 111 (rwx), 5 is 101 (r-x) and 4 is 100 (r--).
- Coursework that asks for binary from octal.
Frequently asked questions
How do chmod numbers map to rwx?
Each octal digit is 3 bits for read, write and execute. 755 is 111 101 101, which is rwx r-x r-x for owner, group and others.
Can I convert negative numbers?
Yes. Put a minus sign in front and it is kept in the result, for example -755 becomes -111101101. The converter does not produce two's complement.
Is there a limit on how big the number can be?
No practical limit. The conversion uses arbitrary precision integers, so long values stay exact. The step-by-step working is shown for numbers up to 24 digits.
Can I convert fractions?
Not with this tool. It converts whole octal numbers to whole binary numbers.
Other number converters
Going the other way? Use the Binary to Octal Converter. To see a number in every base at once, try the all-in-one number converter.