Octal doesn’t come up as often as binary or hexadecimal in everyday computing, but the conversion between binary and octal uses the exact same grouping trick as binary-to-hex, just with groups of 3 digits instead of 4.
Why Groups of 3 Work for Octal
Octal uses 8 symbols, 0 through 7, and 8 is exactly 2 to the 3rd power. That relationship means every single octal digit corresponds exactly to a group of 3 binary digits, the same clean relationship binary and hex share, just with a different group size.
Converting Binary to Octal, Step by Step
Starting from the rightmost digit, split the binary number into groups of 3, padding the leftmost group with extra 0s if it’s short of 3 digits. Convert each 3-digit group directly to its decimal value, which is also its octal digit, since octal digits never exceed 7.
A Worked Example
Converting 101110 to octal: split into two groups of 3, giving 101 and 110. 101 converts to 5, and 110 converts to 6. Combining both groups gives 56 in octal.
A Second Example With Padding
Converting 1011 to octal: this only has 4 digits, so grouping from the right gives 011 and 1, and the second group needs padding to 001. That gives 001 and 011, which convert to 1 and 3 — combining to give 13 in octal.
Converting Decimal to Octal Instead
Decimal to octal doesn’t use the grouping trick directly, since decimal doesn’t divide evenly into binary or octal. Instead, it uses the same repeated-division method as decimal to binary, just dividing by 8 instead of 2 and reading the remainders from bottom to top.
Where Octal Still Gets Used
Octal shows up today mainly in Unix and Linux file permission codes, where a permission setting like “755” is actually three octal digits, each representing a group of 3 binary permission flags (read, write, execute) for the file’s owner, group, and everyone else.
Why This Matters Even If You Never Use Octal Directly
Understanding that binary, octal, and hexadecimal are really just three different ways of grouping the same underlying 1s and 0s makes all three systems less intimidating — none of them requires new math, only a different-sized grouping of digits you already know how to read.
Convert Between All Three Systems
Our binary translator and hex converter are useful references while practicing octal conversions by hand, and our guide on binary to hexadecimal covers the same grouping method applied to base 16.