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The last digit is the check digit "7", and if the other numbers are correct then the check digit calculation must produce 7. Add the odd number digits: 0+6+0+2+1+5 = 14.
The check digit is computed as follows: Drop the check digit from the number (if it's already present). This leaves the payload. Start with the payload digits. Moving from right to left, double every second digit, starting from the last digit. If doubling a digit results in a value > 9, subtract 9 from it (or sum its digits).
For the end user, Code 128 barcodes may be generated by either an outside application to create an image of the barcode, or by a font-based barcode solution. Either solution requires the use of an application or an application add in to calculate the check digit and create the barcode.
Verhoeff had the goal of finding a decimal code—one where the check digit is a single decimal digit—which detected all single-digit errors and all transpositions of adjacent digits. At the time, supposed proofs of the nonexistence [6] of these codes made base-11 codes popular, for example in the ISBN check digit.
The check digit calculation is as follows: each position is assigned a value; for the digits 0 to 9 this is the value of the digits, for the letters A to Z this is 10 to 35, for the filler < this is 0. The value of each position is then multiplied by its weight; the weight of the first position is 7, of the second it is 3, and of the third it ...
To perform the checksum calculation — Take the value (0 through 42) of each character in the barcode, excluding start and stop codes. Sum the values. Divide the result by 10 (for Mod 10 check digit) or by 43 (for Mod 43 check digit). The remainder is the value of the checksum character to be appended.
Finally, the last digit is known as a “check” digit. This is based on a mathematical formula, and it confirms the validity of the card. Other numbers found on a credit card.
The validity of a digit sequence containing a check digit is defined over a quasigroup. A quasigroup table ready for use can be taken from Damm's dissertation (pages 98, 106, 111). [3] It is useful if each main diagonal entry is 0, [1] because it simplifies the check digit calculation.