Hexadecimal

Also called: hex, base 16, base-16

The base-16 number system, with digits 0–9 and A–F (10–15). One hex digit stands for exactly 4 bits, so hex is a compact way to write binary.

Hexadecimal (hex) is base 16. It needs sixteen digit symbols, so after 0–9 it uses letters: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15. Place weights are powers of 16: 1, 16, 256, 4096, …

Hex exists because people are bad at reading long binary. Since 16 = 2⁴, one hex digit is exactly one 4-bit nibble, so converting between hex and binary is a lookup. The 16-bit pattern 1101 0110 0010 1111 is just D62F₁₆.

Where you'll see it:

memory addresses and register contents in a debugger
web colors such as #FF8800 (three bytes: red, green, blue)
machine code, error codes and network hardware addresses

In code, hex is usually marked with a 0x prefix: 0x2F = 2F₁₆ = 47. See base notation.

Conversions:

hex ↔ binary: one digit per 4 bits (binary hex conversion)
hex → decimal: digit × weight, then add (hex decimal conversion)
decimal → hex: repeated division by 16
hex ↔ octal: go through binary (hex octal conversion)

16¹

16⁰

Worked examples

Example

1A3₁₆ to decimal

Multiply each digit by its power of 16.

1.
1 in the 256s place: 1 × 256 = 256.
2.
A (10) in the 16s place: 10 × 16 = 160.
3.
3 in the 1s place: 3 × 1 = 3.
4.
Total: 256 + 160 + 3 = 419.

Example

C5₁₆ to binary

Replace each digit with its nibble.

1.
C = 12 = 1100.
2.
5 = 0101.
3.
Result: 11000101₂. Check: 128 + 64 + 4 + 1 = 197 = 12 × 16 + 5.

Common mistakes

Reading hex digits as decimal: 36₁₆ is 3 × 16 + 6 = 54, not thirty-six.
Writing a remainder of 12 as the two digits "12" instead of the single digit C.
Grouping binary into fours from the left instead of from the right.

Practice Hexadecimal

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Number Systems lesson

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Memory lesson full course

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Hexadecimal is taught in Number Systems.

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