UP student number checksum

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UP student number checksum

The last digit of UP student numbers is a check digit, calculated according to the similar rules as an ISBN 10. ISBN 10 check digit is calculated "so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0" (from Wikipedia). It appears as though the UP check digit does not have a similarly easy check for validity, although the calculation of the check digit is similar up to a point.

The sum

To calculate the check digit for a 7 digit student number, follow this procedure. Take the first digit and multiply by 8, the second by 7, the third by 6 and so on:

Digit 9 7 0 0 8 0 4
i 8 7 6 5 4 3 2
Product 72 49 0 0 32 0 8

Add the products together and call this <math>s</math>. In the example above, <math>s=161</math> The check digit is now <math>(12 - s \mod 11) \mod 10</math>. For the example, we would get <math>(12 - 161 \mod 11) \mod 10 = (12 - 7) \mod 10 = 5</math>.

Student assistants

It appears that "student numbers" for student assistants which start with "04" rather than a number representing the year have a minor alteration to the checksum code - the code calculated above is 1 too large. It is not certain at this point if the same calculation is carried out and 1 subtracted or if the code is calculated with a different modulus.

Code

Awk

This awk program recognises short student numbers at the beginnig of lines and replaces the first field with the long student number

/^s[0-9][0-9][0-9][0-9][0-9][0-9][0-9]/ { 
    split($1, digits, "");
    s = 0
    for (i=2; i<9; i++) 
	s +=  digits[i] * (10-i);
    $1 = $1 (12 - (s % 11)) % 10
}
{print}

Python

This python function calculates the check digit of a short student number passed as a string:

def checkdigit(short):
   # Calculate check digit
   s = sum(int(char)*(8-i) for i,char in enumerate(short))
   return (12 - (s % 11)) % 10


Basic

This Basic function (suitable for calls from MS Excel or OpenOffice Calc), calculates the check digit:

function checkdigit(numstr as variant) as integer
' calculates the check digit (8th number) of a 7 digit student number
   dim i, s as integer
        
   s = 0
   for i = 1 to 7
      s = s + CInt(mid(numstr, i, 1))*(9-i)
   next i
        
   checkdigit = (12 - (s mod 11)) mod 10
end function


Matlab

In Matlab (and possibly octave) it's a one liner that calculates the check digit:

function Check=CheckDigit(str)
% Str is a seven digit string e.g. str='9700804'
Check=mod(mod(12-sum([str2double(cellstr(str'))]'.*[8:-1:2]),11),10)