How to convert binary to octal by hand
Example 1: 111101101 in binary is 755 in octal
Binary to octal: group the bits in 3s
Because 8 = 2³, every 3 bits make exactly one octal digit. Start from the right and pad the leftmost group with zeros if needed.
| 3-bit group | Value | Octal digit |
|---|---|---|
| 111 | 7 | 7 |
| 101 | 5 | 5 |
| 101 | 5 | 5 |
111 101 101 → 755
Example 2: 110100100 in binary is 644 in octal
Binary to octal: group the bits in 3s
Because 8 = 2³, every 3 bits make exactly one octal digit. Start from the right and pad the leftmost group with zeros if needed.
| 3-bit group | Value | Octal digit |
|---|---|---|
| 110 | 6 | 6 |
| 100 | 4 | 4 |
| 100 | 4 | 4 |
110 100 100 → 644
Binary to Octal conversion table
| Binary | Octal | Decimal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 11 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
| 1000 | 10 | 8 |
| 1001 | 11 | 9 |
| 1010 | 12 | 10 |
| 1011 | 13 | 11 |
| 1100 | 14 | 12 |
| 1101 | 15 | 13 |
| 1110 | 16 | 14 |
| 1111 | 17 | 15 |
| 10000 | 20 | 16 |
| 100000 | 40 | 32 |
| 1000000 | 100 | 64 |
| 1100100 | 144 | 100 |
| 10000000 | 200 | 128 |
| 11111111 | 377 | 255 |
| 100000000 | 400 | 256 |
| 1000000000 | 1000 | 512 |
| 1111101000 | 1750 | 1000 |
| 10000000000 | 2000 | 1024 |
Where this conversion comes up
- Turning rwx permission bits into a chmod value: rwxr-xr-x is 111 101 101, which is 755.
- Coursework that asks for octal as a shortcut from binary.
Frequently asked questions
Why group binary digits in threes for octal?
8 is 2³, so every octal digit holds exactly 3 bits. Group from the right and look each group up.
Can I convert negative numbers?
Yes. Put a minus sign in front and it is kept in the result, for example -111101101 becomes -755. 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 binary numbers to whole octal numbers.
Other number converters
Going the other way? Use the Octal to Binary Converter. To see a number in every base at once, try the all-in-one number converter.