Ten digits weren’t enough. So we borrowed from the alphabet.

Sixteen symbols: 0 through 9, then A through F. No mystery — A is just a name for ten, B for eleven, up to F for fifteen. Reach sixteen, carry left.

In 2AF (hexadecimal):

• F → 15 × 1 = 15
• A → 10 × 16 = 160
• 2 → 2 × 256 = 512

Total: 687 in decimal.

Hexadecimal = base-16 — sixteen symbols, positional value, carry at sixteen.

Why not just use octal? Because one byte is eight binary digits — and eight binary digits group perfectly into two hexadecimal digits:

1101 1111 → D F → DF

4 binary digits = 1 hex digit. 8 binary digits = 2 hex digits.

One byte, two characters. Clean, compact, universal. That’s why you see hex everywhere: memory addresses, color codes (#FF5733), error codes, network identifiers. It’s the lingua franca between binary’s precision and human readability.

The Pattern

16⁰ → 16¹ → 16² → 16³ → ...

1 → 16 → 256 → 4096 → ...

Octal bridged binary and humans. Hex replaced it — because a byte deserves exactly two digits.