Number Systems

This conversion is the fastest of the three pairings, because one hex digit always corresponds to exactly one nibble (4 bits).

Binary to hex

1. Split the binary number into nibbles from the right, padding the leftmost group with zeros if needed.
2. Convert each nibble to its denary value (0 to 15).
3. Write each value as a single hex digit.

Example — Convert binary 10110111 to hex.

• Split into nibbles: 1011 and 0111.
• 1011 = 8 + 2 + 1 = 11 = B.
• 0111 = 4 + 2 + 1 = 7.
• Binary 10110111 = hex B7.

Hex to binary

1. Take each hex digit and convert it to a 4-bit binary nibble.
2. Join the nibbles together to form the full binary number.

Example — Convert hex 5F to binary.

• 5 = 0101.
• F = 15 = 1111.
• Combined: 01011111.