Give an example of how a check digit is calculated?

Answer 1

Say you have a list of numbers that you need to send to your friend, either by semaphore, over the phone, on a telegraph, by voice or Morse Code over ham radio, etc.

Let's say the numbers are: 15, 22, 61, 14, 11, 92, 73, 36.

Add up all the digits. Not the numbers, just the individual digits.

The digits add up to 54. Forget the 50. Just keep the 4, and send that along with the list.

If any digit in the list of numbers, or any groupof digits in the list, gets changed on the way, then when your friend adds up all the digits in the list he gets, he won't get the 4.

The only way there could be errors and he could still get the 4 would be if all the errors added up to exactly a multiple of 10, which is possible but very unlikely.

So, by increasing the length of your message by just one digit, you included a very powerful way for your friend to be able to tell whether he received the whole list accurately.

It's not good enough for him to be able to identify or correct errors; but it's plenty good enough for him to know whether or not there has been one, and to ask you to send the list again if the check doesn't add up.

This is the basis for all of the 'error-checking' and 'error-correcting' routines in data communication ... sending some extra characters along with the message, that carry enough extra description of the message so that the receiver can tell when errors have occurred in transmission, and can even correct them without repeating the transmission if the scheme is clever enough.