Extend parity across a byte or block
Use parity-byte and two-dimensional block checks to detect and, in a limited single-bit case, locate an error.
Section 2 · Data transmission
This sequence follows Cambridge IGCSE Computer Science 0478, 2026–2028 syllabus Version 6. It covers subject content sections 2.1–2.3 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
What does a row parity value check?
What you will learn
- Describe a parity byte
- Explain row and column parity in a block check
- Distinguish locating one changed bit from correcting arbitrary errors
Extra parity can check groups of bytes
A parity byte adds parity values for a group of transmitted bytes. In a two-dimensional block check, parity is calculated for each row and each column of a block of bits.
Apply and check the rule
If exactly one bit changes, its row and column can both fail parity; their intersection locates the changed bit. Multiple errors can create ambiguous patterns or escape detection, so block parity is not a guarantee against every error.
Pause and explain
What assumption makes the row-column intersection locate one bit?
Worked example
In a two-dimensional parity block, row 3 and column 5 both fail checks, and only one bit is assumed to have changed. Where is the likely error?
Show the worked solution
- The failed row identifies row 3.
- The failed column identifies column 5.
- Their intersection is the changed bit.
Answer At row 3, column 5
Try a topic test
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.
A block check reports row 2 and column 4 as incorrect. Under the one-bit-error assumption, identify the bit position.
Give me a hint
Use the crossing of the two failed checks.
Compare my reasoning
- The row is 2.
- The column is 4.
- Their intersection is row 2, column 4.
Row 2, column 4
Look for these in your work
- Row identified
- Column identified
- Intersection stated
State one limitation of a parity byte or block parity.
Give me a hint
Consider what happens when more than one bit changes.
Compare my reasoning
- An even number of bit errors may preserve parity.
- Multiple failing rows and columns can make the error position ambiguous.
- Parity does not guarantee that every error is detected or repaired.
Multiple bit changes can evade checks or create ambiguous locations; parity does not guarantee correction.
Look for these in your work
- Multiple errors considered
- Detection/correction limitation stated
A storage link uses two-dimensional parity. One row and one column fail, but the receiver cannot assume there was only one error. What should it conclude?
Give me a hint
The intersection is conclusive only under a single-bit assumption.
Compare my reasoning
- The row and column identify a candidate intersection.
- If multiple bits changed, other patterns can also produce those failed checks.
- The receiver should treat the block as suspect and request reliable recovery rather than claim a certain correction.
The intersection is a likely location only if exactly one bit changed. Without that assumption the pattern may be ambiguous; the block should be treated as erroneous and recovered safely.
Look for these in your work
- Candidate position identified
- Assumption limitation
- Safe response
Common mistakes
- Treating a parity byte as a checksum that guarantees integrity
- Claiming two-dimensional parity can always correct multiple errors
What can you explain now?
How can two-dimensional parity locate a single changed bit?
Compare with the explanation
The failed row and column intersect at the bit
Both checks narrow the error to one position under the single-error assumption.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What extra information does a two-dimensional parity check add over one parity bit?
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.