Learning Objectives
- Explain the purpose of a check digit.
- Describe how a check digit is calculated and verified.
- Explain how check digits detect common data-entry errors.
- Identify ISBNs and bar codes as uses of check digits.
- Distinguish data-entry error detection from transmission error detection.
Key Terms
- Check digit
- A digit calculated from other digits in a code and included so data entry can be checked.
- Data-entry error
- A mistake made while typing, scanning or copying a code.
- ISBN
- International Standard Book Number, which includes a check digit.
- Bar code
- A machine-readable representation of a product or item code that can include a check digit.
- Transposition
- Entering two digits in the opposite order.
- Validation rule
- A rule applied to decide whether entered data is acceptable.
Purpose Of A Check Digit
A check digit is included in an identification number to detect mistakes made when the number is entered. It is calculated from the other digits using an agreed algorithm. The full code, including the check digit, is printed or stored with the item.
When the code is typed or scanned, the receiving system repeats the calculation using the entered digits. It compares the calculated result with the entered check digit. If the values do not satisfy the rule, the system reports that the code is invalid.
A check digit does not prove that the code belongs to the correct person or product. It checks the internal consistency of the digits. A different valid code could still be entered by mistake and pass its own check.
Data-Entry Errors Detected
A single incorrect digit usually changes the calculated result, so the entered check digit no longer matches. A missing or extra digit can also be noticed because the length or positions are wrong.
Many check-digit algorithms are designed to detect common transposition errors, where two neighbouring digits are entered in reverse order. The weighting of positions helps distinguish the altered order. The exact detection ability depends on the algorithm.
The syllabus does not require one universal calculation method. An examination question may provide a method and ask the candidate to calculate or verify a digit. The steps must be followed exactly.
ISBN And Bar-Code Examples
An ISBN identifies a particular edition and format of a published book. Its final character or digit is used as a check digit according to the ISBN rule. When the number is entered, the calculation is repeated to detect a likely typing error.
Product bar codes also contain digits that identify items and include a check digit. A scanner reads the bars, the digits are interpreted and the check calculation is performed. If the check fails, the system can request another scan or manual entry.
The check digit is part of the code but does not contain descriptive product data by itself. Its purpose is checking.
Check Digit Versus Transmission Check
A check digit is mainly associated with data entry. Parity, checksum and echo check are described in this syllabus as methods for checking data after transmission.
The distinction matters in examination answers. If a cashier scans a product code and the system checks the final digit, this is a check-digit process. If a network packet is tested after crossing a link, a transmission error-detection method is being used.
Both approaches use redundancy: extra information is added to help detect mistakes. However, the stage and type of error are different.
Check-Digit Process
| Stage | Action |
|---|---|
| Create code | Calculate check digit from the other digits. |
| Store or print | Include the check digit in the complete code. |
| Enter or scan | Read all digits including the check digit. |
| Recalculate | Apply the same rule to the entered digits. |
| Compare | Reject or warn if the rule is not satisfied. |
Examples And Purpose
| Example | What The Code Identifies | Why A Check Digit Helps |
|---|---|---|
| ISBN | A particular book edition and format | Detects likely typing or scanning errors. |
| Bar code | A product or item | Detects likely read or entry errors. |
Worked Examples
Provided Modulo Rule
Question: A code uses the sum of its first five digits modulo 10 as the check digit. Find the check digit for 47286.
- Add digits: 4 + 7 + 2 + 8 + 6 = 27.
- Find the remainder when 27 is divided by 10.
Answer: 7.
Verifying A Code
Question: Using the same rule, is 314159 valid if the final digit is the check digit?
- Add the first five digits: 3 + 1 + 4 + 1 + 5 = 14.
- 14 modulo 10 is 4.
- Compare calculated 4 with entered final digit 9.
Answer: No. The check fails.
Explaining A Transposition
Question: Why can a weighted check-digit method detect digits 27 entered as 72?
- The two positions have different weights.
- Swapping the digits changes which weight multiplies each value.
- The final calculated result is likely to change.
Answer: The position-sensitive calculation produces a different check result.
Examination Guidance
- State that the digit is calculated from the other digits.
- Mention recalculation and comparison during entry.
- Use ISBN and bar code when examples are requested.
- Do not claim a check digit confirms that an item is genuine or that the correct valid code was selected.
Common Mistakes
- Describing a check digit as encryption.
- Saying the check digit stores the price of a product.
- Confusing a check digit with a checksum sent in a packet.
- Assuming every possible entry error is detected.
Knowledge Check
1. What is the purpose of a check digit?
2. How is it checked?
3. Name two syllabus examples.
4. What is a transposition error?
5. Can a valid but wrong product code pass a check digit?
