Chapter 7 Identification Numbers: How many are enough? If you look carefully around you, you will see batches of numbers examples of identification numbers that you have probably and letters on almost everything: on products in every store, already seen many times. on books, and certainly on the credit cards in your wallet. Even The Universal Product Code The Universal Product Code, or though they may contain letters of the alphabet, these numbers UPC, appears on just about every item you buy from a major are called identification numbers. They serve to identify the product, the book, or the person who owns the credit card. store. It is designed to help the store track inventory and to make Producing identification numbers is a lot more difficult price changes easier. Figure 1 shows three examples. The first is than just deciding to print numbers on products or books, from a box of Bigelow tea, the second is from a box of Xerox toner Every system of identification numbers has a plan that tells cartridges, and the third is from the front page of a newspaper. exactly how to assign those numbers. These plans must There are two parts to the code: a bar code and a UPC number. Notice that the UPC number has 12 digits. The confront several issues. First, there must be enough numbers for all of the things that you expect to number. Since giving the first 6 digits identify the producer and the next 5 digits identify the exact product. The final digit is the check digit. same identification number to different items would defeat the Of the 6 digits identifying the producer, the first digit is purpose of having an identification number, it is important that the plan have a way to give a unique number to each item. particularly important. This digit, which appears at the far left of It is also necessary to be able to check for errors in the the code and is called the number system character, tells the type identification number. This check helps to prevent misidentifying of product. Table 1 lists the number system characters currently in items. As a result, most identification number plans include a use. The numbers 1, 8, and 9 have been reserved for future use. The number, called a check digit, for this purpose. We consider two 5 digits that identify the product can be any digits whatsoever. Once the first 11 digits are known, the check digit is calculated from them. FIGURE 1 Universal Product Codes 7 68663 30909 "95205 60881" 72310 00192 TABLE 1 UPC NUMBER SYSTEM CHARACTERS Standard UPC number (for any type of product) 2 Random-weight items (produce, meats, etc.) 3 Pharmaceuticals 4 In-store marketing (gift cards, store-specific coupons) 5 Manufacturer's coupons 6 Standard UPC number (for any type of product) Standard UPC number (for any type of product) 1. Under the current system, how many different producer numbers are possible? 2. If all digits were allowed for the number system character, how many more producer numbers would be created? 3. How many possible correct UPC codes are there? Assume all possible producer numbers are allowed