Barcodes Here is an example of a UPC-A barcode, taken from Wikipedia: A UPC-A barcode has 12 digits. The first digit is something that tells how the numbers are generally used – for example, a particular industry might use a certain number for certain kinds of items. The last twelfth digit is a check digit that can be used to try to tell whether or not the numbers have an error. This check digit is constructed in a certain way. UPC-A Barcode Check Digit Calculation The check digit is constructed as follows: We have the first 11 digits: $$ABCDEFGHIJK$$ So let \(L\) be the last twelfth digit. We sum the…