Table of Contents Link to heading

• Hexadecimal (Hex) Numbering
• Use Cases
• All Zeros versus All Ones
• Representing Hexadecimals
• Hexadecimal Conversions
  • Conversion Table
  • Binary to Hexadecimal
  • Hexadecimal to Binary
  • Decimal to Hexadecimal
  • Hexadecimal to Decimal
    • Binary Detour
    • Positional Notation
    • Doubling

Hexadecimal (Hex) Numbering Link to heading

a convenient way to represent binary values.

1 hex = 1 nibble = 4 bits = 1/2 byte

Data is often stored using word sizes that are multiples of 4 bits.

Hexadecimal is a base 16 system and uses the numbers 0 to 9 and the letters A/a to F/f.

Use Cases Link to heading

Three basic usages of hex include HTML colour codes, MAC addresses, and IPv6 addresses.

Other possible usage include:

• Extensively used in assembly programming languages and in machine code.
• Often used to refer to memory addresses.
• Can be used during the debugging stage of writing a computer program.
• Used to represent numbers stored in a CPU’s registers or in main memory.

All Zeros versus All Ones Link to heading

Given that 8 bits (a byte) is a common binary grouping, binary 00000000 to 11111111 represent the hexadecimal range 00 to FF.

Representing Hexadecimals Link to heading

Leading zeros are always displayed to complete the 8-bit representation. For example, the binary value 0000 1010 represents 0A in hexadecimal.

Hexadecimal numbers are often represented by a value preceded by 0x (e.g, 0x73 and 0x0A) to distinguish between decimal and hexadecimal values in documentation.

Hexadecimal may also be represented using a subscript 16 or by using the hex number followed by an H (e.g., 73H and 0AH).

Hexadecimal Conversions Link to heading

Conversion Table Link to heading

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

Binary to Hexadecimal Link to heading

Break the binary value into groups of 4 and convert every group to one hex digit (add zeros to the left end of the binary number to create groups of four if needed).

0011 1011₂ = 3B₁₆

1. 0011₂ = 3₁₆
2. 1011₂ = B₁₆

Hexadecimal to Binary Link to heading

Take each hexadecimal digit and find the binary equivalent.

3B₁₆ = 0011 1011₂

1. 3₁₆ = 0011₂
2. B₁₆ = 1011₂

Decimal to Hexadecimal Link to heading

Decimal :right_arrow: binary :right_arrow: hexadecimal

59₁₀ = 0011 1011₂ = 3B₁₆

1. 0011₂ = 3₁₆
2. 1011₂ = B₁₆

Hexadecimal to Decimal Link to heading

Binary Detour Link to heading

Hexadecimal :right_arrow: binary :right_arrow: decimal

3B₁₆ = 0011 1011₂ = 59₁₀

Positional Notation Link to heading

Since there are 16 digits, each position represents a power of 16.

2A4F₁₆ = 2×16³ + 10×16² + 4×16¹ + 15×16⁰ = 10831₁₀

Doubling Link to heading

Take each leftmost value (converted to decimal), multiplied by 16 and added to the next value.

2A4F₁₆

1. 0×16 + 2 = 2
2. 2×16 + 10 = 42
3. 42×16 + 4 = 676
4. 676×16 + 15 = 10831₁₀