Hex to Decimal Conversion: Understanding Number Systems

The Four Number Systems in Computing

Computers work with different number systems, each with a different base:

• Binary (Base 2): Uses only 0 and 1. The language computers actually think in.
• Octal (Base 8): Uses 0–7. Historically used in computing; still appears in Unix file permissions.
• Decimal (Base 10): Uses 0–9. The number system humans use daily.
• Hexadecimal (Base 16): Uses 0–9 and A–F. Commonly used in programming, color codes, and memory addresses.

Why Hexadecimal?

Hexadecimal is a convenient shorthand for binary. Because 16 = 2^4, each hex digit represents exactly 4 binary bits. A byte (8 bits) can be written as exactly 2 hex digits. This makes hex much more readable than long strings of 0s and 1s while still mapping directly to binary.

Example: Binary 11111111 = Hex FF = Decimal 255

Hexadecimal Digit Reference

Decimal	Hex	Binary
0	0	0000
1	1	0001
5	5	0101
9	9	1001
10	A	1010
11	B	1011
12	C	1100
13	D	1101
14	E	1110
15	F	1111
16	10	00010000
255	FF	11111111

How to Convert Hex to Decimal

Multiply each hex digit by 16 raised to the power of its position (starting from 0 on the right).

Example: Convert 2A hex to decimal

2A = (2 × 16^1) + (A × 16^0) = (2 × 16) + (10 × 1) = 32 + 10 = 42

Example: Convert 1F4 hex to decimal

= (1 × 16^2) + (F × 16^1) + (4 × 16^0) = (1 × 256) + (15 × 16) + (4 × 1) = 256 + 240 + 4 = 500

Where You See Hexadecimal

• Web colors: #FF5733 is hex for red=255, green=87, blue=51
• Memory addresses: 0x7FFD4A8B in debugger output
• MAC addresses: 00:1A:2B:3C:4D:5E (each pair is one byte)
• Hash values: SHA-256 checksums, MD5 hashes
• Unicode code points: U+1F600 (emoji)
• HTML/CSS color codes: #3B82F6 (blue)

Converting Decimal to Hex

Divide the decimal number by 16 repeatedly and record remainders in reverse:

Example: Convert 255 to hex
255 ÷ 16 = 15 remainder 15 → F
15 ÷ 16 = 0 remainder 15 → F
Reading remainders bottom-up: FF