Hex vs Octal

The whole argument in one fact

A byte is eight bits. Eight divides by four, giving two hex digits exactly. Eight does not divide by three, so an octal digit never lines up with a byte boundary.

one byte in hex     FF        two digits, exact
one byte in octal   377       three digits, and the first is
                              only using one of its three bits

That is the entire reason hex won. It is not fashion or convention — it is arithmetic, and it became decisive the moment hardware standardised on eight-bit bytes.

Side by side

Why octal existed in the first place

Octal was not a mistake. It was the right answer to a different hardware question.

Before eight-bit bytes became standard, machines used 12, 18, 24 and 36-bit words — all divisible by three. On a 36-bit machine, a word is exactly twelve octal digits, and octal is the natural shorthand. It also needs no letters, which mattered on the limited character sets and printers of the era.

The IBM System/360 in 1964 settled on the eight-bit byte, the industry followed, and the arithmetic changed sides.

Where octal still makes more sense

Octal survives wherever the underlying fields really are three bits wide, and Unix file permissions are exactly that.

chmod 755

  7 = 111  owner:  read, write, execute
  5 = 101  group:  read,        execute
  5 = 101  others: read,        execute

the same value in hex: 1ED  — which tells you nothing

Three permission groups, three bits each, three octal digits. The notation matches the structure exactly. Hex would split those fields across digit boundaries and make the whole thing unreadable, which is a neat demonstration that the best base depends entirely on the width of the thing you are describing.

The leading-zero trap

In C and the many languages that copied its syntax, a leading zero marks an octal literal. This is a genuine and long-standing source of bugs.

int a = 010;   // eight, not ten
int b = 08;    // compile error — 8 is not an octal digit
int c = 0x10;  // sixteen, unambiguously hex

Modern languages prefer an explicit 0o prefix for precisely this reason. Python 3, Rust and JavaScript all use 0o10, which cannot be misread.

Converting between them

There is no digit-level shortcut, because three and four do not divide into each other. Both go through binary.

1. Expand each digit to its bit pattern — four bits for hex, three for octal.
2. Join the bits into one string.
3. Regroup from the right into the size the target base needs.
4. Pad the leftmost group with zeros if it is short.
5. Read each group as a digit in the new base.

The hex to octal converter and octal to hex converter do this for any length, and the reference table lists every byte.

Landmarks in both

The last row shows when the two do agree: every twelve bits, because twelve is the first number divisible by both three and four.

Frequently asked questions

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