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LIGN 17 Final Review Sheet
March 11, 2011
Error Detecting Codes:
For each of the systems we’ve discussed in class, you should be able to describe and
implement the algorithm it uses; you should also be able to describe what kinds of errors
it can catch/correct, and what kinds of errors (if any) it misses.
1. Compute the check digit for the following 3 Credit Cards, using the Luhn Algorithm:
4217 8989 5432 724 ?
5239 2349 8723 657 ?
3339 2348 9992 66 ?
2. If the underlined digit in each of the following cases is incorrect, what number belongs
in its place? Once again, use the Luhn algorithm to determine the correct answer. (Note:
these numbers were generated haphazardly. It is possible that the underlined number is
actually correct.)
8237 4443 89
04 6213
6123 787
8 4326 4127
7521 8882
6634 1111
3. Complete the following table, and answer the questions below:
Credit Card Digit
Contribution to Luhn Sum
Even Position
Odd Position
0
1
2
3
4
5
6
7
8
9
Which two digits, if they are adjacent and transposed, will the Luhn algorithm not catch?
Why is this clear from the table above?
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3. Determine the check digit for the UPC’s below:
423467883 ?
234876544 ?
567234535 ?
4. If the underlined digit in each of the UPC’s below is incorrect, determine what its
correct value should be:
9
342398377
44444
44447
624894
7537
5. What kinds of transposition errors will UPCs not be able to catch?
6. Will either of the above systems be able to catch nontransposition errors that effect
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 Winter '08
 Kehler
 Coding theory, check digit, Variablelength code, spectral test

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