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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

  1. Split the binary number into 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.

Hex to binary

  1. Take each hex digit and convert it to a 4-bit nibble.
  2. 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