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Today I want to publish a code for checksum calculation by modulus 10.

This algirithm is very popular for UPC barcodes (Universal Product Code), hash code or serial number generation for applications etc...

The basic algorithm:

1. add the values of the digits in the odd positions (1, 3, 5...)
2. multiply this result by 3
3. add the values of the digits in the even positions (2, 4, 6...)
4. sum the results of steps 2 and 3
5. the check digit is the smallest number which, when added to the result in step 4, produces a multiple of 10.

Small example. Assume the source data is 08137919805

1. 0+1+7+8+5=22
2. 22*3=66
3. 8+3+9+9+0=29
4. 66+29=95
5. 95+??=100 where ?? is a 5 (our checksum)

My implementation in the Pascal:

function Mod10(const Value: string): Integer;
var
  i, intOdd, intEven: Integer;
begin
  {add all odd seq numbers}
  intOdd := 0;
  i := 1;
  while (i < Length(Value)) do
  begin
    Inc(intOdd, StrToIntDef(Value[i], 0));
    Inc(i, 2);
  end;

  {add all even seq numbers}
  intEven := 0;
  i := 2;
  while (i < Length(Value)) do
  begin
    Inc(intEven, StrToIntDef(Value[i], 0));
    Inc(i, 2);
  end;

  Result := 3*intOdd + intEven;
  {modulus by 10 to get}
  Result := Result mod 10;
  if Result <> 0 then
    Result := 10 - Result
end;

You can expand this algorithm for own needs.

For example, I modified it and\par now I use it for any characters (not only digits) in source value.
The original algorithm I use for UPC-barcode validation in the SMReport Designer and the my extended algorithm I use in the serial number generation as part of the protection schema (in the shareware projects).

Published: October 24, 2001

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