Octal to binary converter

Octal to binary table

The last rows are the largest 32-bit and 64-bit unsigned values. The second is past the point where ordinary JavaScript numbers start rounding; the table and the converter above both compute with BigInt, so every digit is exact.

How to convert octal to binary

Replace each octal digit with its 3-bit binary value, keeping the leading zeros inside each group — octal 1 is 001, not 1 — and join the groups in order. For 255: 2 → 010, 5 → 101, 5 → 101, giving 010 101 101, which is 10101101 once the leading zeros are dropped. Nothing is carried from one digit to the next, so a long octal number converts as easily as a short one.

Octal and binary side by side

The largest 16-bit value is 177777 in octal and 1111111111111111 in binary: 6 digits against 16. Every octal digit is exactly 3 bits, so the lengths stay in a fixed ratio and any stretch of digits can be converted without looking at its neighbours. Binary is what bit masks, flags and subnet masks are reasoned in: a /24 network mask is twenty-four 1 bits followed by eight 0 bits, 255.255.255.0 once written in decimal. In JavaScript and Python source, 173 is written 0o255 in octal and 0b10101101 in binary. Paste a prefixed number into the converter and it switches to the matching base; a number with no prefix is read in the selected base — octal on this page.

Other conversions

Going the other way? Binary to octal converter.

• Octal to decimal
• Octal to hex
• Decimal to binary
• Hex to binary

Or open the full number base converter and see a number in all four bases at once.