Math for Liberal Studies
Dr. Galluzzo
Section 3.3: More Check Digit Systems
Universal Product Code (UPC)
A UPC is 12 digits long. The 12th digit is a check digit. Compute a weighted sum of all 12 digits
with weights 3, 1, 3, 1, etc. If the weighted sum ends in 0, then the UPC is valid.
1. Determine the check digit that should be appended to the UPC 0-14300-25433-.
2. Find an object that has a UPC on it and verify that it is valid.
3. Commit a substitution error with your object’s code and show that the UPC check digit scheme
detects the error.
4. Commit a transposition error with your object’s code. Does the UPC check digit scheme detect
this error?
Bank Routing Numbers
A bank routing number is 9 digits long. The 9th digit is a check digit. Compute a weighted sum of
all 9 digits with weights 7, 3, 9, 7, 3, 9, etc. If the weighted sum ends in 0, then the routing number
is valid.
5. Determine the check digit that should be appended to the bank routing number 01500085.
6. A suspicious check has routing number 198102957. Is the routing number valid?
Math for Liberal Studies
Dr. Galluzzo
International Standard Book Number (ISBN)
There are 10 digits, including the check digit. Use the weights 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 on all of
the digits of the ISBN, including the check digit. The check digit should be chosen so that the
weighted sum is evenly divisible by 11. If the digit would need to be 10, then “X” is used instead.
7.
Suppose that the ISBN 0-1750-3549-0 is incorrectly reported as 0-1750-3540-0. Is this error
detected by the ISBN check digit scheme?
8.
Suppose that you know that the ISBN 0-6690-3925-4 is the result of the transposition of two
adjacent digits, but not involving the first or last digits. Determine the correct ISBN.
The Luhn Algorithm
There are 16 digits, and the 16th digit is a check digit. Compute a weighted sum using weights 2, 1,
2, 1, etc., except that whenever multiplying by two would result in a two-digit number, record the
sum of those digits instead. The ID number is valid if the sum of these “products” ends in 0.
9.
Use the Luhn algorithm to determine the check digit for the number 3001 2560 0196 431.
10.
Determine whether the Master Card number 3541 8232 0033 2273 is valid.
Math for Liberal Studies
Dr. Galluzzo
Solutions
1.
5.
6.
7.
9
9
No, the check digit should be 9
Yes
8.
9.
10.
0-6690-9325-4
2
Yes