Convert between binary and hexadecimal
Group binary digits into four-bit nibbles so each group converts directly to one hexadecimal digit.
This sequence follows Cambridge IGCSE Computer Science 0478, 2026–2028 syllabus Version 6. It covers subject content sections 1.1–1.3 only. The separately published 2029–2031 syllabus is not mapped here. Practice is original, self-checked and does not award an official Cambridge grade. Full timed papers and human subject-teacher review remain outstanding.
Before you begin
- No programming language is required. Be comfortable with place value and multiplication; each lesson introduces the computer-science notation it uses.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many binary bits correspond to one hexadecimal digit?
What you will learn
- Convert positive binary and hexadecimal values in both directions
- Group bits from the right into nibbles
- Explain why hexadecimal is a compact, readable representation
One hexadecimal digit maps to four bits
Four bits make 16 possible patterns, matching the 16 hexadecimal digits. Split a binary value into groups of four from the right. Add zeros at the left only when needed to complete the first group.
Apply and check the rule
Hexadecimal is shorter and less error-prone for people to read or copy than a long binary string. It is used in contexts such as memory dumps, network addresses and colour codes. It does not change the underlying data.
Pause and explain
Why is 7A a useful shorthand for a binary pattern?
Worked example
Convert 10111100₂ to hexadecimal.
Show the worked solution
- Group from the right: 1011 1100.
- 1011 is 11, which is B; 1100 is 12, which is C.
- Check: BC₁₆ = 11×16+12 = 188.
Answer BC₁₆
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Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 11100101₂ to hexadecimal.
Give me a hint
Group into nibbles from the right.
Compare my reasoning
- Split into 1110 and 0101.
- 1110=E and 0101=5.
E5₁₆
Look for these in your work
- Groups 1110 and 0101
- Hex digits E and 5
Convert 6D₁₆ to eight-bit binary.
Give me a hint
Convert each digit separately to four bits.
Compare my reasoning
- 6 becomes 0110.
- D=13 becomes 1101.
- Join the two nibbles.
01101101₂
Look for these in your work
- Each digit mapped to four bits
- Eight-bit result correct
A technician must compare two 24-bit memory addresses by eye. Explain one advantage of writing them in hexadecimal and how to check the conversion.
Give me a hint
Relate each hex digit to a fixed-size bit group.
Compare my reasoning
- Each four-bit group becomes one hexadecimal digit.
- The address is written with fewer characters, reducing visual clutter.
- Convert each hex digit back to four bits to verify the original pattern.
Hexadecimal is a shorter, easier-to-read form of the same binary address. Each hex digit can be checked as its four-bit nibble.
Look for these in your work
- Four-bit relationship stated
- Readability benefit stated
- Verification method given
Common mistakes
- Grouping bits from the left when the length is not a multiple of four
- Adding padding zeros to the right and changing the value
What can you explain now?
What is 1110₂ in hexadecimal?
Compare with the explanation
E
1110 is 14, represented by E.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why do you pad the left of a binary value, rather than the right, before grouping into nibbles?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.