Question

3 Check Digits: ISBN In this problem, we'll look at a real-world applications of check-digits International Standard Book Numbers (ISBNS) are 10-digit codes (did2...dio) which are assigned by the publisher. These 10 digits contain information about the language, the publisher, and the number assigned to the book by the publisher. Additionally, the last digit dio is a "check digit" selected so that1 i di 0 (mod 11). (Note that the letter X is used to represent the number 10 in the check digit.) (a) Suppose you have a very worn copy of the (recommended) textbook for this class. You want to list it for sale online but you can only read the first nine digits: 0-07-288008-? (the dashes are only there for readability). What is the last digit? Show your work. di (mod 11) (b) Wikipedia says that you can determine the check digit by computing Show that Wikipedia's description is equivalent to the above description (c) Prove that changing any single digit of the ISBN will render the ISBN invalid. That is, the check digit allows you to detect a single-digit substitution error (d) Can you switch any two digits in an ISBN and still have it be a valid ISBN? For example, could 012345678X and 015342678X both be valid ISBNS? Explain

Please tell me whether my answers are correct or not. If not please tell me why and give me a guide to solving the problem correctly. Thanks!

Answer 1

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