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Octal to Binary Converter

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Convert an octal number to binary. Each octal digit expands to exactly three binary digits — for example 755 in octal becomes 111101101 in binary, where each 3-bit group encodes one Unix permission triplet (rwx, r-x, r-x). Useful for decomposing chmod and umask values into the individual read, write and execute flags they represent. Long octal strings are handled exactly using BigInt internally.

From (Octal (8))

Octal (8)

Allowed: 0–7

To (Binary (2))

Binary (2)

Allowed: 0 and 1

Octal (8) → Binary (2)

Quick reference table

Octal (8)	Binary (2)
7	111
10	1000
100	1000000
777	111111111
1000	1000000000
7777	111111111111

Glossary

Octal (base 8)

The octal numeral system uses digits 0 through 7. It was popular in early computing because each octal digit maps cleanly to exactly three binary digits, which made it convenient for systems with 12-, 24- or 36-bit words. Today its most common surviving use is Unix file permissions: chmod 755 means owner-rwx, group-rx, others-rx, where each digit is a 3-bit permission mask.

Binary (base 2)

The binary numeral system uses only two digits — 0 and 1 — and is the native number system of every digital computer. Each binary digit (bit) represents a power of 2: the rightmost bit is 2^0 = 1, then 2^1 = 2, 2^2 = 4, 2^3 = 8 and so on. Eight bits form one byte. Binary underlies every memory cell, register and network packet.

Related tools

Binary to Octal

Convert binary (base 2) to octal — every 3 bits become 1 octal digit

Octal to Decimal

Convert octal numbers (base 8) to decimal — handy for Unix permissions

Octal to Hex

Convert octal (base 8) to hexadecimal (base 16) — exact integer mapping

Number Base Converter

Convert integers between binary, octal, decimal and hexadecimal — with full BigInt support