Understanding Hexadecimal Math and Base Systems
Hexadecimal is a Base 16 numbering system. Unlike our everyday Base 10 decimal system that uses ten symbols (0–9), hexadecimal uses sixteen symbols: 0–9 for values zero to nine, and the letters A–F for values ten to fifteen.
Positional Values in Base 16
To convert a hexadecimal number to decimal, multiply each character by its positional power of 16, starting with 16⁰ on the far right. For example, the hex value A5 converts to decimal like this:
(A × 16¹) + (5 × 16⁰)
= (10 × 16) + (5 × 1)
= 160 + 5 = 165
Hexadecimal Conversions
Because 16 is a power of 2 (2⁴), conversions between hexadecimal and binary are incredibly simple. Each hex digit corresponds exactly to a 4-bit binary group (called a nibble):
Hex: 1 0001
Hex: 9 1001
Hex: A (10) 1010
Hex: F (15) 1111