8. Hexadecimal

Hexadecimal

Hexadecimal

Hexadecimal is a **base-16** numbering system.

• It uses 16 digits, 0 to 9 and then A to F.
• Each position corresponds to $16^n$.
• Since $2^4=16$, it is easy to convert between binary and hex.

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To convert a binary number to hexadecimal (or back):

• We group each part of the binary number into groups of 4 bits (a Nibble).
• Convert each separate nibble to decimal.
• Each nibble translates to one hexadecimal character.

For example, to convert $100111011110_2$ to hex:

• Group into nibbles: $100111011110$
• Convert each nibble to decimal: $91314$
• Translate to hex characters: $9\text{D}\text{E}$
• Hence $9{\text{DE}}_{16}$