### CENTRE for INNOVATION inMATHEMATICS TEACHING

BAR CODES

Most grocery products include an identifying Bar Code on their wrappers and many supermarkets now use these bar codes for totalling sales at the checkout, using a light pen to read the code.

 Problem 1 What advantages are there for the grocery trade in using bar code technology?Are there disadvantages?

The UPC (Universal Product Code) was introduced in America in 1973 and adapted to form EAN (European Article Code) in 1974. There are two versions of EAN - 13 digit and 8 digit, but we will deal with the 8 digit version. An example is shown below.

This version is used by stores such as Sainsbury or Boots to code their own label products.

The Number is divided into three parts

 00 34600 9 retailers' code product code check digit

The check digit is chosen so that

3 x (1st + 3rd + 5th+ 7th number) + (2nd + 4th + 6th + 8th number)

is exactly divisble by 10.

Problem 2 Do the following 8 digit EAN codes have the correct check digit?
 a) 00034548 b) 00396349 c) 50168622

Problem 3Find the check digit, x, for the following 8 digit EAN codes
 a) 0008639x b) 5021421x c) 0042655x

 Another 8 digit EAN is shown opposite. It has left and right hand guard bars and centre bars. In between there are 8 bars of varying thickness. Each number is represented by a unique set of 2 bars and 2 spaces. As can be seen in the magnified version of 5, each number code is made up of 7 modules.We write 5 as 0110001 to indicate whether a module is blank (0) or black (1).

All left hand numbers start with 0 and end with 1, and only use a total of 3 or 5 black modules. Right hand numbers are the complement of the corresponding left hand code e.g. right hand 5 = 1001110.

 Problem 4 Design all possible left hand codes using these rules and use the examples on this worksheet to identify the code for each number.

 Extension If each digit is made up of 8 modules, rather than 7, how many possible left hand codes now exist?

 Other Material Try out an online bar code editor and checker here.There is a page to help you find all the left-hand codes here.