The Universal Product Code Check Digit Scheme

Preliminary Activity. Many of the products that are sold in stores have a 12-digit Universal Product Code (UPC) associated with them. Find four or five examples of 12-digit UPCs. Given the work on check digit schemes in the previous two sections, and the fact that the last of the 12 digits in a UPC is the check digit, attempt to determine the UPC check digit scheme. 

There is a Universal Product Code (UPC) on every product in every store. UPCs are used in a variety of ways. First of all. a UPC identifies not only the product but also what type of product it is and its manufacturer. Using the UPC. each store specifies a price that appears on the cash register when the product s bar code is scanned as you check out. Stores also use UPCs for inventory purposes. By using the UPC, the store can track products that sell quickly, or ones that rarely sell, and make sure that all products are always in stock. 

In this section, the 12-digit Version A system will be studied. In a 12-digit UPC 01-0203040506-070800010011-012, the first digit oi, referred to as the number system character identifies the type of product. Table 2.1 lists the different values of oi and when each is used. 

Definition 2.6.1. Given the ll-digit number ai-a2a3a4a5a6-a7aga9aioau, the check digit a 2 is appended to create the UPC Oi-a2a3a4a5O6-O7O8O9ai0flu-oi2 such that 012 satisfies the equation 

The UPC 3-70501-09110-4 is invalid, because the calculation below results in a false statement (39 s= 3 10 -i- 9)  

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The Universal Product Code Check Digit Scheme... 

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