Link to the host of this site- Marist College This project was supported by a grant (DUE #9752632) from the National Science Foundation.
            
    Preliminary Activity: Create a list of at least five different types of identifying numbers taken from a variety of different sources (e.g., product labels, magazines, and book covers). Look at all the identification numbers collected, paying special attention to the lengths of each number, the types of characters used, and other defining characteristics. Write a short summary of your findings.

      Identification numbers are used to identify individual items, specific products, people, accounts, or documents. Social security numbers, driver license numbers, credit card numbers, International Standard Book Numbers (ISBN), Universal Product Codes (UPC), and bank account numbers are all examples of identification numbers. In addition, numbers are used to identify passports, US Postal money orders, UPS packages, library books, merchandise, and many other items. 
      Identification numbers are used for a variety of purposes. Not only are they used for easy identification of products, documents, or accounts, but for tracking and inventory purposes. For example, UPS numbers are not only used to identify specific packages, but also to track the packages. Each package that a customer sends is assigned a number so that the customer knows when the package was picked up, where it is at any point in time, and when the package is delivered. UPCs, found on most products, are used in a variety of ways. First of all, a UPC not only identifies the product, but also the type of the product and its manufacturer. Each store associates a price with the UPC that appears on the cash register when the product's bar code is scanned at the check-out counter. Stores also use UPCs to keep track of inventory.  
      An identification number usually takes the form of a string of digits, letters, symbols, or some combination of them. A digit is a number 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, and a symbol is an object such as *, /, #, & or $. Together, digits, letters, and symbols, form the characters that are used to create identification numbers. 
      Every day, identification numbers are presented over the phone, copied onto documents, scanned and entered into computers, or transmitted by some other method. Each time this happens, there is a chance that one or more digits in the number will change or move when it is transmitted from one location to the other. For example, the UPC 0-53600-10054-0 on a product could be scanned into the computer as 0-53600-10059-0 or 0-53600- 10045-0. In either case, an error in the number has occurred. In addition, less than honest individuals sometimes attempt to forge certain identification numbers for personal profit.  
      It is important to ensure that identification numbers are transmitted correctly, and in certain cases, not forged. Transmission errors can occur when bar codes are scanned incorrectly, when numbers are written or typed in the wrong order, or when phonetic mistakes (eg: one person says ``sixteen" and the other hears ``sixty") are made. Table #1 lists the most common types of errors and their relative frequency. 
 
Table #1
  
  

      All this motivates the following goal: To develop methods that will recognize when an identification number has been transmitted incorrectly! These methods, called check digit schemes, are not that difficult to develop. In fact, there are even algorithms that identify errors and then correct the error that was made. 
      Most check digit schemes append an extra digit or digits, called a check digit(s), to the number generated for a product, document, etc, and then use that digit(s) to check for errors after the number has been transmitted. The check digit can appear in any position in the number. However, it is often appended to the end of the number and is the last digit(s) in the identification number.  






     Paper Assignment: You are employed by an organization that wants to use a check digit scheme. At this point, you are familiar with a variety of schemes. An initial survey done by the company has reduced the choices down to two schemes, the ISBN and Verhoeff schemes. Your colleague recommends the ISBN scheme, but you believe that the Verhoeff scheme is better for the organization. Write a report that not only recommends the Verhoeff scheme but also refutes your colleague's earlier recommendation.

     To do this, compare both schemes in a report called a feasibility study, paying attention to the following factors:
  • ease of use (the length, time involved with, and complexity of the calculations)
  • strength (in terms of the errors it can detect)
  • flexibility (the ISBN scheme is designed for an identification number of a fixed length while the Verhoeff scheme can be manipulated and adjusted to an identification number of any length).

      At the end of this comparison, you should recommend the Verhoeff scheme and state your reasons for doing so.

      Paper Assignment: You are employed by an organization that wants to use a check digit scheme. At this point, you are familiar with a variety of schemes. An initial survey done by the company has reduced the choices down to two schemes, the IBM and Verhoeff schemes. Your colleague recommends the IBM scheme, but you believe that the Verhoeff scheme is better for the organization. Write a report that not only recommends the Verhoeff scheme but also refutes your colleague's earlier recommendation.

    To do this, compare both schemes in a report called a feasibility study, paying attention to the following factors:

  • ease of use (the length, time involved with, and complexity of the calculations)
  • strength (in terms of the errors it can detect)
  • flexibility (both the IBM and Verhoeff schemes are designed for an identification number of any length).
     At the end of this comparison, you should recommend the Verhoeff scheme and state your reasons for doing so.