Check Digit Calculation
Introduction and Use

The check digit table provides the information needed to calculate check digits using Dual Mod 10, Arithmetic Mod 10, Arithmetic Mod 11, Geometric Mod 11 and Geometric Mod 10 algorithms.

Number your existing OCR scan line, for all characters to be included in the check digit calculation, from left to right starting with number “one”. 

Match each corresponding number, from left to right, with a number in the column titled “Field digits left to right” on the Check Digit Calculation Weight Table. 

Select the algorithm that you wish to use to calculate your check digit.  Go to the corresponding column for your selected check digit algorithm.  Under each of the corresponding number positions on the OCR scan line (column titled “Field digits left to right”) write the number in the corresponding row as it appears under the column of your selected check digit algorithm. 

For example:  If you have selected Dual Mod 10 you will place a 2 under the left most character to be used in the calculation of the check digit.  Under the second character or the character to the immediate right of the first character place a 1.  Continue until a weight value has been placed under each character to be used in the calculation of the check digit.

Multiple the weight value times the value of the character immediately above it in the scan line.

Add the sum of all the products of the multiplication.

Divide the sum of the products by the number of the value of your check digit.  For a Mod 10 divide your product by 10.  For a Mod 11 divide your product by 11.  Carry your division only to the ones place.  Determine the remainder if any.

Example:  The product sum is 112.

• Dual Mod 10 = 112 / 10 = 11 Remainder 2

• Arithmetic Mod 10 = 112 / 10 = 11 Remainder 2

• Arithmetic Mod 11 = 112 / 11 = 10 Remainder 2

• Geometric Mod 11 = 112/ 11 = 10 Remainder 2

• Geometric Mod 10 = 112 / 10 = 11 Remainder 2

If the product sum is 110

• Dual Mod 10 = 110 / 10 = 11 Remainder 0

• Arithmetic Mod 10 = 110 / 10 = 11 Remainder 0

• Arithmetic Mod 11 = 110 / 11 = 10 Remainder 0

• Geometric Mod 11 = 110/ 11 = 10 Remainder 0

• Geometric Mod 10 = 110 / 10 = 11 Remainder 0

Using the Remainder Table find your remainder under the column titled “Remainder”. 

Move to the right on the row where you found your remainder until you are under the column of the check digit algorithm that you used.

The character found at the intersection of the row and column is the check digit for the characters that you included in your check digit routine.

Example: You want to calculate an Arithmetic Mod 11 check digit for the following series of numbers:    32174215

¹These numbers are the digits in the scan line.  You will be calculating a ninth digit that will be added to the right of the last digit.  This ninth digit will be the check digit.

²The sequence number is the location of the scan line digit within the scan line.  The sequence number is used to reference the weight value from the Check Digit Calculation Weight Table.

³This number is retrieved from the Check Digit Calculation Weight Table.  The weight digit corresponds to the intersection of the row representing Sequence and the column representing the selected check digit routine (Arithmetic Mod 11 in this example).

⁴This number is the product of Number ¹ times Weight ³.

⁵This is the running sum of the results in the Product ⁴ line.  The final sum is the number that will be used in calculation of the check digit.

• Divide the sum 106 by 11.   106 / 11 = 9 Remainder 7.

• Using the Remainder Table look under the column titled Remainder.  Find the number 7.

• Now move across the row where the 7 is located on to the column titled Arithmetic Mod 11.  The number in this location (4) is the Arithmetic Mod 11check digit for the string of numbers 32174215.