You would have to talk to the person that wrote the algorithm to
calculate the check digit when they printed out the serial numbers in
the first place (production line process, etc.). Normally, a check digit
is included on serial numbers and sometimes on part numbers also, to
prevent (or catch) incorrect data entry. In other words, if a customer
calls in for tech support, and accidentally transposes 2 digits while
reading the number over the phone, then without the check digit, how
would anyone know that an error has been made?

This check digit process is to prevent fraud, wrong spare parts from
being dispatched, and a whole range of errors, etc.

It is not really safe to be re-generating the check digit, if it has not
been included in the data you are getting. How will you know that a
digit is wrong or transposed?

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Regards,
Bill Renaud