0984
Number Systems
Data Representation · 4 question types
Exam Frequency Analysis
Past paper frequency (2018 to 2024)
This topic accounts for approximately 12% of your exam marks.
stable
High
Stable12%
Binary/hex conversion and binary arithmetic appear in every Paper 1. Consistently 8 to 15 marks.
This conversion is the fastest of the three pairings, because one hex digit always corresponds to exactly one nibble (4 bits).
Binary to hex
- Split the binary number into from the right, padding the leftmost group with zeros if needed.
- Convert each nibble to its denary value (0 to 15).
- Write each value as a single hex digit.
Hex to binary
- Take each hex digit and convert it to a 4-bit nibble.
- Join the nibbles together to form the full binary number.
Worked example
Converting binary to hexadecimal
Convert the binary number 10110100 to hexadecimal.
Solution:
- Split into nibbles from the right: 1011 | 0100
- Left nibble 1011: 8 + 2 + 1 = 11 → hex digit B
- Right nibble 0100: 4 → hex digit 4
- Result: B4