Check digits explained: how barcodes catch a typo with one number

EAN-13 and UPC-A barcodes terminate with a digit that holds no information; it's a verification number known as the check digit. This digit helps a scanner or code detect most typing errors instantly.

For EAN-13, the process begins with the initial 12 digits. Each digit is then multiplied by either 1 or 3, alternating starting with 1 from the left. All the resulting products are summed. The check digit is the number that, when added to this sum, makes it a multiple of 10.

For example, consider the digits 400638133393. Multiplying them alternately by 1 and 3 gives: 4+0+0+18+3+24+1+9+3+9+9+9=89. The check digit is determined by subtracting the remainder of 89 divided by 10 from 10, then applying the operation again if necessary. In this case, the check digit is 1, making the full code 4006381333931.

In JavaScript, this process can be coded into a function. The function takes the first 12 digits as input, multiplies each by either 1 or 3, sums the products, and then calculates the check digit.

UPC-A uses a similar method, but it starts the weighting with 3 instead of 1 for the first digit. This scheme is designed to catch any one incorrect digit, although it may not catch all swaps of two adjacent digits. Some other systems, like ISBN-10, use a different method, applying a mod 11 calculation that can identify adjacent swaps. Credit card numbers, on the other hand, use a different algorithm known as the Luhn algorithm.

Barcodes are a simple yet effective system for error detection, but they're not foolproof. Other systems trade accuracy for complexity, providing stronger protection against errors.