a digit that is the product of a series of mathematical operations on the first digits that help doublecheck that the other digits are correctly entered into a system when typed manually or barcode scanned

a mathematical derivation of the numbers which precede it, so running this mathematical calculation on the number in question will tell if it's valid

a mathematical function that computes a single, unique value for any input

a mathematical function that depends on the full contents of the packet, like the one-way functions used for authentication

An additional character added to a bar code providing a mathematical method for determining the integrity of the bar code. Not all bar code types support a checksum. Of the bar code types that do, some support an optional checksum while others support a mandatory checksum.