Error Detection — Parity & Checksum

Syllabus & Goals 3 min

Cambridge 2.2 · Methods of error detection Paper 1 · Computer Systems

By the end of this lesson you can:

1. Explain why transmitted data must be checked for errors.
2. Use a parity check (even and odd) and a parity block to find an error.
3. Describe a checksum and an echo check.

Recap / Warm-Up 5 min

Packets can be corrupted on the way — by electrical interference, switching problems or skewing. The receiver must be able to spot a corrupted byte.

Quick starter

How many 1s are in the byte 01101100? Is that an even or odd count?

Key Concept 14 min

1 · Parity checks

A parity check counts the number of 1-bits in a byte. One bit (usually the most significant) is reserved as the parity bit and set so the total is even (even parity) or odd (odd parity).

Sender and receiver agree the parity first. If a byte arrives with the wrong parity, an error is detected.

2 · Parity blocks (2-D parity)

Send a block of bytes plus a parity byte. Check parity along every row and every column. The error sits at the intersection of the faulty row and faulty column — so you can find and fix it.

3 · Checksum and echo check

Worked Example 12 min

(a) Set the even-parity bit

The 7-bit value 1101100 has four 1s — already even. So for even parity the parity bit is 0, giving 0 1101100. For odd parity it would be 1.

(b) Detect a transmission error

Even parity was agreed. A byte arrives as 01001100 — that is three 1s (odd). The parity has changed from even to odd, so an error is detected.

The parity check as an algorithm

Cambridge pseudocode

// Work out the EVEN parity bit for a 7-bit value
DECLARE Bits : ARRAY[1:7] OF INTEGER
DECLARE Index, Ones, ParityBit : INTEGER
Bits ← [1, 1, 0, 1, 1, 0, 0]
Ones ← 0
FOR Index ← 1 TO 7
    IF Bits[Index] = 1
        THEN
            Ones ← Ones + 1
    ENDIF
NEXT Index
IF Ones MOD 2 = 0
    THEN
        ParityBit ← 0
    ELSE
        ParityBit ← 1
ENDIF
OUTPUT "Even parity bit is ", ParityBit

The same algorithm in Python (IDLE)

# Work out the even parity bit for a 7-bit value
bits = [1, 1, 0, 1, 1, 0, 0]
ones = sum(bits)
if ones % 2 == 0:
    parity_bit = 0
else:
    parity_bit = 1
print("Even parity bit is", parity_bit)

Output

Even parity bit is 0

Try It Yourself 12 min

📝 Exam Practice 10 min

Recap & Key Terms 3 min

A parity check counts 1-bits and uses a parity bit (even/odd) to flag a changed byte; a parity block finds the exact bit at a row/column intersection. A checksumrecalculates a value over a block, and an echo check sends the data back to compare.

Parity check

Checking the count of 1-bits against an agreed even/odd parity.

Parity block

A 2-D parity check over rows and columns that locates the exact bit in error.

Checksum

A value calculated from a data block, recalculated by the receiver to detect errors.

Echo check

Sending received data back to the sender to compare with the original.

Homework 1 min

Task (≤ 15 min): Even parity is used. For each 7-bit value, give the parity bit: (a) 1110000, (b) 1011011, (c) 0000001.