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Error Detection

Data Transmission · 4 question types

Practise

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 5% of your exam marks.

stable
Rare
Stable5%

Parity bits, checksums and check digits each appear in most papers. Often 3 to 4 marks.

A parity block combines a horizontal parity bit (one per byte) with a vertical parity byte (one bit per column), so that the row AND column of any single-bit error can be identified.

Two-dimensional parity block: four data bytes stacked as rows of a bit grid, with a redundant parity byte (LRC) calculated down each column shown beneath, and the transmitted frame of the four data bytes followed by the appended column-parity byte 01001111 sent to the receiver.
Source: LRC by GeeksforGeeks

The structure:

  • A block of (say) nine 8-bit bytes, arranged as 9 rows × 8 columns.
  • Each row has its own parity bit, calculated across the row's data bits.
  • A 10th row, called the parity byte, holds one parity bit per column, calculated down the column.

When the block is received, the receiver re-calculates every row parity and every column parity. The intersection of the mismatched row and the mismatched column pinpoints the exact bit that flipped, which can then be corrected automatically.

What parity blocks detect

  • Single-bit error: detected AND located.
  • Two errors in the same row: row parity passes, but two columns mismatch (still detected, harder to locate).
  • Even number of errors in the same row AND same columns: undetectable.

Parity blocks are far stronger than a single parity bit, at the cost of one extra byte per block.