Communication, Codes and Cyphers

Homework 1 - Basics

1. Mathematical Basics:
   1. What is the value of log₁₀ 1000 ?
   2. What is the value of log₂ 17 ?
   3. log₂ 0.125
   4. What is the value of 2^-4 ?
   5. What is the probability of rolling a 2 or 3, and then a 5 in two rolls of a (fair) die?
   6. What is the probability of rolling a total of 5 on two rolls of a (fair) die?
   7. The probability that a letter chosen at random from an English language text is the letter 'E' is about 0.131. How many times would you expect the letter 'E' to occur in a book containing 1,000,000 letters?
   8. List the first 10 prime numbers.
2. Modulo Arithmetic:
   1. Write out the addition and multiplication tables for arithmetic mod 7
   2. What is 7 + 5 + 4 mod 9 ?
   3. What is 7 x 5 x 4 mod 11 ?
   4. What is 7 + 5 x 3 mod 9 ?
   5. What is 55 - 32 mod 16 ?
   6. What is 3/7 mod 11 ?
3. Introductory Examples of Codes:
   1. Choose a passage of English of about 25 letters length and encode it using:
      1. Morse code.
      2. ASCII.
      3. The substitution cypher given by the following permutation:

         ABCDEFGHIJKLMNOPQRSTUVWXYZ
         CLXWJKQAYUMIETZBHOPSDVFNGR

   2. - · / - - - / · - - / / · · / · · · / / - / · · · · / · / / · - - / · · / - · / - / · / · - · / / - - - / · · - · / / - - - / · · - / · - · / / - · · / · · / · · · / - · - · / - - - / - · / - / · / - · / - / /
   3. The following is in ASCII. Decode it.

      1001010 1100111 1101110 1101110 1110001 0100000 1011011 1110001 1110100 1101110 1100010 0100001

   4. What is the correct last digit for the ISBN 0-11-735-924-?
4. Shannon's model of communication:
   1. Explain how data written to and read from from a computer hard drive fits Shannon's model.
   2. Explain why a "tin can telephone" does not fit Shannon's model.
5. Extra Credit: This is from a class I taught previously, and I don't recall what it says! One question's extra credit will be given for the first student who deciphers this and explains why they think they know what it says.

   RT BYL NQS YOPSQKNZM BYL PEYLDI OS NODS MY ISWYIS MERP CSPPNHS OB DYYURZH NM MES TQSVLSZWRSP YT MES SZWYISI DSMMSQ NZI OB N ORM YT SILWNMSI HLSPPJYQU