Pries: M467 - Information and Coding Theory, Spring 2013
Review problems
1. Roman 1.1: Modular arithmetic and strings. #3, 4, 6, 12, 13.
A) The first nine digits of the ISBN for a book are 0-312-59034. What is the check
digit?
B) You have 9 stacks of 9 coins, all of which appear to be identical. One of these stacks
is made up of all fake coins, while the rest of them are real gold. The real coins weigh
10 grams each, while the counterfeits weigh 9 grams each. You have a scale that will
tell you the mass of any combination of the coins, but you want to be clever and find
out which stack contains the fake coins in the least possible number of weighings. How
do you do it?
2. Roman 1.2: Codes. #2, 5, 6.
3. Roman 1.3: Uniquely decipherable codes and McMillan’s Theorem. #1, 4, 6, 8.
4. Roman 1.4: Instantaneous codes and Kraft’s Theorem. #9, 10, 15, 16.
5. Roman 2.1: Average length. #1, 3, 4, 5.
6. Roman 2.2: (not on Quiz 1) Huffman encoding. #3, 4, 9, 10. Extra credit #7, 13.