What is a check digit?

A check digit is an extra digit calculated from the other digits of a code and added to the end of it, so that a keying error in the code can be detected automatically.

Name two kinds of keying error a check digit is designed to catch.

A check digit is designed to catch a single digit typed wrongly and two adjacent digits typed the wrong way round.

Why is 11 used as the modulus?

The number 11 is prime, and because every digit carries a different weight, any single-digit error and any swap of two digits changes the weighted total, so no such error can slip through.

Which weights are used in the Modulus 11 calculation?

The digits are weighted from the right, the rightmost digit of the code being multiplied by 2, the next by 3, the next by 4 and so on.

Set out the steps of the Modulus 11 calculation.

Each digit is multiplied by its weight, the products are added, the total is divided by 11 to give a remainder, and that remainder is subtracted from 11 to give the check digit.

CCEA A-Level Digital Technology 2650

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Data, Information and Data Representation

Check digits and the Modulus 11 method

3 things to know
AS Unit 2

Overview

What a check digit protects against, weighting the digits and taking the remainder to eleven, writing ten as X, and testing a code for validity including a transposed pair.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

Modulus 11 is applied to the code 1236. Show that the check digit is X.

Key term

The valid code 12343 is mis-keyed as 21343. Show that the Modulus 11 test detects the error.

Key term

What is the purpose of a check digit?

Questions from this subtopic

Each one with the model answer underneath.

1
What is a check digit?
Model answer
A check digit is an extra digit calculated from the other digits of a code and added to the end of it, so that a keying error in the code can be detected automatically.
2
What is the purpose of a check digit?
Model answer
A check digit lets a program recalculate the expected digit from the code just entered and compare it with the digit typed, which catches a mis-keyed code at the moment of entry.
3
Name two kinds of keying error a check digit is designed to catch.
Model answer
A check digit is designed to catch a single digit typed wrongly and two adjacent digits typed the wrong way round.
4
Why is 11 used as the modulus?
Model answer
The number 11 is prime, and because every digit carries a different weight, any single-digit error and any swap of two digits changes the weighted total, so no such error can slip through.
5
Which weights are used in the Modulus 11 calculation?
Model answer
The digits are weighted from the right, the rightmost digit of the code being multiplied by 2, the next by 3, the next by 4 and so on.
6
Set out the steps of the Modulus 11 calculation.
Model answer
Each digit is multiplied by its weight, the products are added, the total is divided by 11 to give a remainder, and that remainder is subtracted from 11 to give the check digit.

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