Error Checking: ISBN

Many products in the modern world are identified with a unique code so that information about them can be stored in a computer system and quickly retrieved. Books, for example, are identified by a unique 13 digit code known as the ISBN (International Standard Book Number - an ISBN had 10 digits up to 2007). Other products such as baked beans and bread are identified by a UPC (Universal Product Code), practically every item in a modern supermarket has its own unique UPC.

These unique numerical identifiers come in handy when checking out of a supermarket or ordering a book and scanning devices have been invented to read the numbers quickly and efficiently. This involves the representation of the numbers as bar codes and scanning with a bar-code scanner. But what if a number is misread? What if a loaf of bread is identified as a bottle of champagne? ISBN and UPC codes have a built-in error check so such a mistake can be spotted and the item can be re-scanned. These provide fairly simple examples of error-checking mechanisms.

Checking ISBN-10 for Errors

Example: ISBN 1-85626-646-X

Enter this code into the search bar of Amazon or Google. Try changing the digits, for example 856 to 865 (an easily-made error when typing) or 646-9. How does this checking work?

The last digit is the check digit. In this case the check 'digit' is 'X' which stands for 10 (as in Roman numerals). The other check digits are 0-9 and the check digit is derived by a process that involves dividing by 11. The full method is as follows:

  1. Write down the first 9 digits in a column or row.

  2. Write the numbers 10-2 under these numbers.

  3. Multiply the pairs of numbers i.e. 1*10, 2*8, 3*5 and so on.

  4. Add up these products.

  5. Divide the total by 11 and note the remainder

  6. Subtract the remainder from 11 - this is the check digit.

When the check digit in the ISBN is multiplied by 1 the sum of the products will divide exactly by 11 with zero remainder.

Implement an ISBN check in a spreadsheet.

UPC codes have a similar check digit method. Did you ever wonder why you can't make up credit card numbers for on-line transactions? There are checks on those too so they can't be made up.