2.1.6 Hexadecimal

Why Hexadecimal?

Hexadecimal (base 16, abbreviated "hex") uses sixteen digits: 0–9 and A–F (where A=10, B=11, C=12, D=13, E=14, F=15). It is used in computing because it provides a compact, human-readable way to represent binary data.

One hexadecimal digit represents exactly four binary bits (a nibble). This means 8-bit bytes are expressed as just two hex digits, 16-bit values as four, and so on — far more readable than a long binary string.

Where hex is used	Example
Memory addresses	`0x1A3F` — far more readable than 16 binary digits
Colour codes (HTML/CSS)	`#FF5733` — three 8-bit colour channels in 6 hex digits
Machine code / assembly listings	Instructions and operands displayed as hex bytes
MAC addresses and IPv6	`2001:0db8:85a3::8a2e`
Error codes	`0x0000007E` — Windows BSOD codes

Converting Between Hexadecimal and Binary

Because 16 = 2⁴, conversion between hex and binary is direct — each hex digit maps to exactly four binary bits.

Hex	Denary	Binary (4 bits)	Hex	Denary	Binary
0	0	0000	8	8	1000
1	1	0001	9	9	1001
2	2	0010	A	10	1010
3	3	0011	B	11	1011
4	4	0100	C	12	1100
5	5	0101	D	13	1101
6	6	0110	E	14	1110
7	7	0111	F	15	1111

Group the binary number into nibbles (4 bits) from the right. Convert each nibble independently to its hex digit.

Example: 10110111 01001110 → hex

1011 = B 0111 = 7 0100 = 4 1110 = E
Result: B74E

Replace each hex digit with its 4-bit binary equivalent. Always write all four bits — including leading zeros.

Example: 3F → binary

3 = 0011 F = 1111 Result: 00111111

Example: A9 → binary

A = 1010 9 = 1001 Result: 10101001

Key Takeaways

Hexadecimal uses 16 digits: 0–9 and A–F. One hex digit = 4 binary bits (one nibble).
Hex is used in computing because it is more compact and readable than binary.
Binary → hex: split into groups of 4 from the right; convert each group.
Hex → binary: expand each hex digit to 4 bits, always keeping leading zeros.