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IGCSE · Practice questions · Check digits and automatic repeat query (ARQ)

Weights of one and three.

Six original Cambridge-style questions on check digits and ARQ, with worked solutions.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Recalculate and compare.

01
Explain
[3 marks]

Describe how a check digit is used to detect errors when a product barcode is scanned.

  • The check digit is calculated from the other digits and stored as the last digit of the barcode. ✓
  • When the barcode is scanned, the check digit is recalculated from the other digits using the same algorithm. ✓
  • If the recalculated digit does not match the scanned check digit, an error has occurred and the barcode is rescanned (or typed in). ✓
02
Calculate
[2 marks]

The ISBN-13 check digit is calculated using the method in this lesson. Calculate the check digit for the ISBN that begins 979824681357. Show your working.

  • Products: 9, 21, 9, 24, 2, 12, 6, 24, 1, 9, 5, 21; total = 143. ✓
  • 143 MOD 10 = 3; check digit = 10 − 3 = 7. ✓
03
Analysis
[3 marks]

A librarian enters the ISBN 9780141306144. The correct ISBN is 9780141036144. Show how the check digit detects the error and name the type of error.

  • Recalculate from the first 12 digits entered (978014130614): total = 92. ✓
  • 92 MOD 10 = 2, so the check digit should be 8, but 4 was entered: the error is detected. ✓
  • It is a transposition error (two digits, 0 and 3, swapped). ✓
04
Recall
[2 marks]

Give two types of data entry error that a check digit can detect.

  • An incorrect digit (one digit entered wrongly). ✓
  • Transposed digits / an omitted digit / an extra digit (any one). ✓
05
Explain
[5 marks]

Describe how automatic repeat query (ARQ) is used to make sure data is received without error.

  • The receiver checks the received data for errors (using an error detection method). ✓
  • If there is no error, the receiver sends a positive acknowledgement to the sender. ✓
  • If there is an error, the receiver sends a negative acknowledgement and the sender resends the data. ✓
  • The sender starts a timer (timeout) when the data is sent. ✓
  • If no acknowledgement is received before the timeout, the data is resent automatically; this continues until a positive acknowledgement is received. ✓
06
Analysis
[2 marks]

A student says: "A check digit is the best way to check that a file has been transmitted correctly over the internet." Explain why the student is wrong.

  • A check digit detects errors in data entry (typing or scanning a number), not errors in transmission. ✓
  • A transmission error check such as a parity check, checksum or ARQ should be used instead. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.