Binary to Octal Converter

The three-bit grouping method

Split the binary string into groups of three bits starting from the right. Pad the leftmost group with leading zeros if it is short, then replace each triple with its octal digit. Take 10110111:

10 110 111         ← raw bits
010 110 111         ← pad left to a full triple
 2   6   7
result → 267

The whole conversion is pure substitution. This is exactly how octal earned its place in computing: it compresses binary into a third of the characters while keeping a clean bit alignment.

The triple lookup table

Only eight rows to remember — and they double as the Unix permission triples, where 111 = rwx (7), 101 = r-x (5) and 100 = r-- (4).

Padding and permissions

As with hex grouping, always count from the right so the least significant group is complete. A 9-bit permission mask divides perfectly into three octal digits, which is why chmod codes are exactly three digits long. If you start with the binary of a permission set — say 111101101 — grouping gives 111 101 101 = 755, instantly readable as rwxr-xr-x.

Where it's used

• Translating raw permission bitmasks into chmod octal codes.
• Shortening binary constants in older systems and assemblers.
• Teaching base conversion alongside the hex nibble method.
• Reading binary data on platforms that traditionally favored octal.