Identification numbers with check digit algorithms 
Portuguese ID Card
The most important identification document of a Portuguese citizen is the identity card BI ("Bilhete de Identidade").
Each BI card has an identification number (on the back, top left) which remains the same throughout the individual's life (even if the BI is renewed because of other reasons, for example, change of marital status or residence).
Given the importance of BI, it is very important that the use and transmission of this number occur without errors. This is the main purpose of the check digit* appended to the identification number (in a small square). Note that with the kind of big numbers as in BI cards, the possibility of someone to transcribe them with errors is real.
How is the check digit of BI calculated?
(*) There is a strong belief among many people that this number rather indicates the number of individuals with the same name as the person holding the respective BI, which is of course false. If you think a little, who does not know someone with some unusual name whose check digit is quite large (eight or nine)? And the opposite case? What about people whose check digit is zero? And what happens when the number of individuals with a given name is bigger than ten? Has anyone seen a BI check digit with more than one digit?
