The ISBN Check Digit Scheme

Preliminary Activity. All books have a ten-digit ISBN associated with them, which is usually printed on the back cover. Find four or five examples of ISBNs. Given the work on check digit schemes in the previous three sections and the fact that the last of the ten digits in an ISBN is the check digit, attempt to determine the ISBN check digit scheme. 

Example 2,7,1, Each of the following ISBNs begins with a 0, indicating that all were published in an English-speaking country, 

The third number in the ISBN is the code that the publisher has chosen for the book. Note in the examples above that a longer publisher code leaves fewer digits available for book titles. Thus a publisher who has a large number of book titles will want a shorter publisher code. The last number is always a single digit and is the check digit. 

For example, the following two ISBNs are used to identify Neal Koblitz s book A Course in Number Theory and Cryptography [14  

The equation presented above in Definition 2.7.2 is often written as follows  

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Definition 2.7.2. The ISBN Check Digit Scheme [4], (251. For the ten-digit ISBN denoted ai 020304asaearagogaio, the check digit a 10 that is appended to the nine-digit number 010203040306070309 is determined by the equation... 

Using the ISBN check digit scheme, determine which of the following is a valid ISBN and which is invalid. 

The number 5-283-11980 has been generated by a publisher to identify a book that it plans to market. Using the ISBN check digit scheme, assign a check digit to this number. Be sure to identify the check digit and the entire ISBN number. 

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