Binary to Octal Converter
Type a base-2 number and get its octal form, three bits per digit.
Octal
| Binary | Decimal | Hex | Octal |
|---|
Going the other way? Use the octal to binary converter.
To convert binary to octal, split the bits into groups of three from the right and replace each group with its octal digit. The number 110101 splits into 110 and 101, which are worth 6 and 5, so the answer is 65.
How it works
Octal is base 8, and eight is two cubed. That makes every group of three bits correspond to exactly one octal digit, the same clean relationship hex has with groups of four. Conversion is a lookup, not a calculation: split, substitute, done.
Worked example with 110101. Counting from the right, it splits into 110 and 101. The group 110 is worth 4 + 2, which is octal digit 6. The group 101 is worth 4 + 1, octal digit 5. Read the digits in order: 65. Cross-check: the whole binary number equals 53 in decimal, and octal 65 means 6 eights plus 5 ones, which is also 53.
Always group from the right. If the leftmost group comes up short, pad it with leading zeros; they cost nothing. Grouping from the left shifts every boundary and produces a wrong answer that still looks plausible, which is the sneakiest error in this conversion.
Octal was big on early computers whose word sizes were multiples of three bits, and it survives today mainly in Unix permissions, where each digit bundles a read, write, and execute bit. When you see chmod 755, you are reading three octal digits: 7 grants all three permission bits, 5 grants read and execute. This converter is exactly the decoder ring for that notation.
The 3-bit table: all 8 octal digits
| Binary | Octal | Decimal |
|---|---|---|
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
FAQ
How do I convert binary to octal?
Group the binary digits into sets of three starting from the right, then replace each group with its octal digit. The number 110101 splits into 110 and 101, worth 6 and 5, so the octal form is 65.
Why three bits per octal digit?
Because eight is two to the third power. Three bits have exactly eight possible patterns, and octal has exactly eight digits, 0 through 7. Each pattern maps to one digit with nothing left over, so conversion is straight substitution, the same trick hex plays with four bits.
Where is octal actually used?
Mostly in Unix file permissions, where a command like chmod 755 packs three read-write-execute bits into each octal digit. It also appears in some older network and aviation systems. Hex has largely replaced it elsewhere because bytes split evenly into two hex digits but not into octal.