Convert binary to octal by splitting the bits into 3-bit groups – each group is one octal digit 0-7. Octal was the classic shorthand before hex took over.
Show calculation steps
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Three bits, one digit
Octal stands to binary as hex does, one power lower: 8 = 2³, so bits group in threes and each triple is one octal digit 0–7. The conversion is regrouping by table — exact, unbounded, and instant.
Octal predates hex as the printout shorthand of 12-, 24- and 36-bit machines, whose word sizes divide by three. It survives wherever its alignment still fits — most famously Unix permissions.
Worked example
Input: 110101111 Group in threes: 110 101 111 Translate: 110→6 101→5 111→7 Result: 657
| Octal digit | 3-bit binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
The permissions connection
A Unix mode is nine permission bits — three rwx triples — and each triple is exactly one octal digit. rwxr-xr-x is 111 101 101, i.e. 755. Every chmod value decodes with the eight-row table above, which is why octal refuses to die.
Why hex won everywhere else
Bytes are eight bits: two clean nibbles for hex, but two-and-two-thirds octal digits. Octal groupings straddle byte boundaries on byte-addressed machines, so hex took the crown when 8-bit bytes standardised. Knowing both means reading both eras of documentation.
Exactness and privacy
Structural regrouping cannot err: any bit length converts exactly, with left-padding shown in the steps. Invalid digits are reported by position, mismatched prefixes redirected to the right tool. Local computation only.
How to use the Binary to Octal Converter
- Paste the binary number.
- Click "Convert to octal".
- The steps show the left-padding and the 3-bit grouping – octal digits span 0-7, exactly three bits each.
- Copy the octal result.
Frequently asked questions
Why three bits per octal digit?
Because 8 = 2³. Three bits cover 0-7 exactly, so binary-to-octal is pure regrouping: 110 101 111 → 657. No division, no rounding, no size limit.
Where is octal still used today?
Chiefly Unix file permissions (chmod 755), where each octal digit is one rwx triple – owner, group, other. It also survives in some escape sequences and older protocol documentation from the era of 12/24/36-bit machines.
What if my bits do not divide into threes?
Left-pad with zeros: 110101111 is already nine bits (three groups); 1101 becomes 001 101 → 15. The steps show the padding applied to your input.
Why did hex largely replace octal?
Byte alignment. A byte is 8 bits – two clean hex digits but 2⅔ octal digits, so octal groupings straddle byte boundaries awkwardly. On 8-bit-byte machines hex simply fits better.
Can the input carry a 0b prefix or spaces?
Yes, both are accepted and stripped. An 0o or 0x prefix is rejected with a pointer to the right converter, protecting you from a silent base mix-up.
How do I check a result by hand?
Recompute one group: the middle group of 110 101 111 is 101 = 5, matching the middle digit of 657. Any single group verifies independently – a property unique to power-of-two base pairs.
Is the conversion local to my browser?
Entirely – the regrouping happens in page JavaScript, and your bits never leave the device.
