Difficulty: Easy
Correct Answer: All of the above
Explanation:
Introduction / Context:
A self-check digit is an extra digit appended to an identifier (such as a product code, customer number, or account ID) that is computed from the other digits using a known rule. Its purpose is to help detect common data-entry and recording mistakes before they propagate into downstream processing, billing, or reporting.
Given Data / Assumptions:
Concept / Approach:
Check-digit schemes compute a function f(d1, d2, ..., dn) that yields the final digit cd. At validation time, the system recomputes cd and compares it with the entered check digit. If they differ, the code is flagged as invalid. Well-known examples include UPC/EAN (mod 10 with weights), ISBN-10 (mod 11), and Luhn (mod 10). These methods are particularly effective at catching single-digit errors and many adjacent swaps; they also catch a portion of more random mistakes, though not all possible multi-error combinations.
Step-by-Step Solution:
Verification / Alternative check:
Empirical analyses of Luhn and mod 11 schemes show near-total detection of single-digit errors and strong detection of adjacent transpositions, validating their practical usefulness for routine data-entry control.
Why Other Options Are Wrong:
Common Pitfalls:
Assuming check digits catch all possible multi-error scenarios; relying on them alone without format and range checks; mis-implementing the weighting or modulus rule.
Final Answer:
All of the above
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