Practice 2 (Digital Codes-Check Digit Systems)

Modular Arithmetic Practice

prepared by:

Joseph Malkevitch
Department of Mathematics and Computing
York College (CUNY)
Jamaica, New York 11451

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

Carry out the following computations, always writing your answer as a value from 0 to the (modulus -1).

1.

a. 76 ? mod 23 b. 45 ? mod 14 c. -24 ? mod 9 d. -23 ? mod 5

b. 76 ? mod 11 b. 45 ? mod 13 c. -24 ? mod 18 d. -23 ? mod 9

c. 79 ? mod 23 b. 41 ? mod 14 c. -29 ? mod 9 d. -26 ? mod 5

2. Determine the check digits for the following ISBN numbers:

3. Take 4 books you own and verify that the ISBN numbers on the books are legal.

4. Determine the check digits for the following UPC codes on common products:

a. 0 37000 38590 ? (answer 5)

b. 0 50428 82973 ? (answer 8)

c. 0 72463 00020 ? (answer 0)

d. 7 29906 11953 ? (answer 0)

5. Determine the check accuracy of the UPC codes (12 digits) on 5 products you find around your house.

6. Find some objects around you home that do not have UPC codes with 12 digits. What do these objects have in common? Why do you think that it was necessary to have a different system for the UPC code on these objects?

7. Here are two proposed credit card numbers. Are they legal? If not, what should the proper check digit be:

a. 4532 3599 2111 6701

b. 5421 5567 2991 7788

8. Is the following a legal number for a postal service money order?

63025566710

(What should the last digit be to make it a correct number?)

9. What should be the value of the ? for the Visa Travel's Check numbers below:

a. 567239023?

b. 458134076?

10. Is the following a legal airline ticket number?

a. 6813468

b. 5124854

c. 7707270