AQA 7517 · Paper 2 · 4.5.4b

Parity Bits &
Check Digits

Error detection in data transmission · Section 4.5

WHAT YOU'LL LEARN

Even/odd parity · Parity worked examples · Check digits (EAN, ISBN) · Limitations

AQA SPEC LINK

4.5.4 — Error detection: parity bits, check digits

Why Error Detection?

Data Errors During Transmission

When data is transmitted (over networks, USB, etc.) individual bits can flip from 0 to 1 or 1 to 0 due to electrical interference, signal degradation, or hardware faults.

Sent: 0100 0001 (letter A)

Received: 0100 0011 (letter C) — bit 1 flipped!

Without error checking, the corruption goes undetected

Parity bits and check digits help detect (but not always correct) such errors

Parity Bits

Even & Odd Parity

EVEN PARITY

A parity bit is added so the total number of 1s in the byte (including parity bit) is even.

ODD PARITY

A parity bit is added so the total number of 1s is odd.

The parity bit is typically the most significant bit (leftmost). Both sender and receiver must agree on which system to use.

Worked Example

Calculating Parity Bits

Example: Data = 1001011 (even parity)

Count 1s in data: 1,0,0,1,0,1,1 → four 1s

Four is already even → parity bit = 0

Full byte: 01001011

Example: Data = 1011010 (even parity)

Count 1s: 1,0,1,1,0,1,0 → four... wait, that's even → parity bit = 0

Actually: 1+0+1+1+0+1+0 = 4 ones → parity bit = 0

Error Detection

How Parity Detects Errors

Sent (even parity): 01001011 → 4 ones (even ✓)
Received: 01101011 → 5 ones (odd ✗)
Error detected! The receiver knows corruption occurred.

Limitation: If TWO bits flip, the parity count stays even — the error is not detected. Parity cannot correct errors, only detect (some) of them.

Check Digits

Check Digits on Barcodes

A check digit is a digit added to the end of a code (barcode, ISBN, bank sort code) to help detect keying or scanning errors

ISBN-13 (books) and EAN-13 (products) use the same check digit scheme

Calculated from the other digits using a mathematical formula

If a digit is mis-scanned, the check digit won't match — error detected

EAN-13 Example

EAN-13 Check Digit Calculation

EAN-13: digits 1–12 alternate ×1 and ×3 weighting
Sum the products, then: check digit = (10 − (sum mod 10)) mod 10

Example first 12 digits: 500012345678
5×1 + 0×3 + 0×1 + 0×3 + 1×1 + 2×3 + 3×1 + 4×3 + 5×1 + 6×3 + 7×1 + 8×3
= 5+0+0+0+1+6+3+12+5+18+7+24 = 81
Check digit = (10 − (81 mod 10)) mod 10 = (10 − 1) mod 10 = 9

Comparison

Parity vs Check Digits

Feature	Parity Bit	Check Digit
Used for	Binary data transmission	Numeric codes (barcodes, ISBNs)
Added value	1 bit (0 or 1)	Single digit (0–9)
Detects	Single-bit flip	Transpositions, single errors
Corrects?	No	No

AQA Exam Style

Practice Question

AQA 7517 — Paper 2 Style

(a) A computer uses even parity. Data byte (excluding parity) is 1010011. State the parity bit and give the complete 8-bit byte transmitted. [2]
(b) The byte 01011010 is received. Using even parity, determine whether an error occurred. Show your working. [2]
(c) Give ONE limitation of using parity bits for error detection. [1]

[5 marks]

2 marks

(a) 1s in 1010011 = four (even) → parity bit = 0. Full byte: 01010011

2 marks

(b) Count 1s: 0,1,0,1,1,0,1,0 = 4 ones. Four is even → no error detected [1]; byte appears valid [1]

1 mark

(c) If two bits flip the parity is still even so the error is undetected / parity cannot locate or correct errors

Summary

Key Points to Remember

Even parity — parity bit chosen so total 1s (including it) is even

Odd parity — parity bit chosen so total 1s is odd

Parity limitation — can't detect even-numbered bit flips; can't correct errors

Check digits — appended to barcodes/ISBNs; detect transcription and scanning errors

Neither parity bits nor check digits can correct errors — see Hamming codes for correction

🎉 Lesson complete — move to the quiz!