Hex to Octal

You have typed hexadecimal without thinking twice about it — every MAC address and every IPv6 address is written in hex. Octal is the base you almost never see, yet the two are cousins, both built from grouping binary digits, and converting between them is a genuinely different exercise from converting either one to decimal.

Two bases, two different ways of grouping bits

Hexadecimal groups binary into chunks of four bits, because four bits gives exactly sixteen combinations, 0000 through 1111. Octal groups binary into chunks of three bits, because three bits gives exactly eight combinations, 000 through 111.

Both are just compact stand-ins for binary. The reason you cannot swap a hex digit for an octal digit directly is that four and three do not share a common factor with each other in the way that matters here — you have to expand back to binary first, then regroup.

Why the two groupings never line up on a byte

A byte is eight bits, and eight divides evenly by four, so a byte is always exactly two hex digits, 00 to FF. Eight does not divide evenly by three, so a byte in octal needs three digits and does not use the full range of them — it runs 000 to 377.

Take the maximum byte value. Decimal 255 is hex FF, a clean two digits. In binary it is 11111111. Regroup that same binary from the right into threes — 011 111 111 — and you get octal 377, since (3 × 64) + (7 × 8) + 7 = 255. Same number, three digits instead of two, and an awkward leading 3 instead of a full range.

Converting hex to octal by hand

1. Convert each hex digit to its 4-bit binary equivalent.
2. String all the 4-bit groups together into one continuous binary number.
3. Starting from the right, regroup the binary digits into chunks of three, padding the leftmost group with zeros if needed.
4. Convert each 3-bit group to its octal digit, 0 through 7.
5. Read the octal digits left to right for the final answer.

Small values across all four bases

Hex to octal questions