Final answer:
The correct statement about check digits is that they are designed to detect transcription and transposition errors, and they are vital for verifying the integrity of data codes.
Step-by-step explanation:
The correct statement about check digits is that they are designed to detect transcription and transposition errors. Check digits are additional digits added to the end of a sequence of numbers, which can be used to verify the integrity of the number sequence. The use of check digits is a form of error detection that is applied in various contexts such as the Universal Product Code (UPC), International Standard Book Number (ISBN), and bank account numbers.
Check digits work by applying a mathematical calculation to the original number. The result of this calculation determines what the check digit should be. When the number sequence is later re-entered or processed, the check digit is recalculated to ensure it matches the original. If it doesn't, an error is indicated.
Contrary to one of the statements, check digits can affect processing efficiency, as they require additional computational steps. However, the benefits of reducing errors often outweigh the minor impact on processing times.