Part 2: Applications of Modular Arithmetic Barcodes on products were introduced in 1973. The barcodes are machine readable versions of the UPC (Universal Product Code). The UPC consist of a 6-digit company code, a 5-digit product code and 1 check digit. To determine the correct check digit: 1) Add the digits in odd positions and multiply the total by 3. 2) Add the digits in even positions. 3) Add the results from steps 1 and 2 4) The total in step 3 must be equivalent to 0 mod 10, which is another way of saying that the result is divisible by 10.