Tasks

1. (2 pts) Chapter 4 Projects and Problems: 5
• also convert your real tag answer to binary
2. (2 pts) Chapter 4 Projects and Problems: 6
3. (4 pts) Assume a 2 symbol input alphabet (a₁, a₂} with probabilities {.6, .4}, respectively.  Use arithmetic encoding (without scaling) to derive a binary encoding of  the following two strings:
1. a₁ a₁ a₂
2. a₂ a₂ a₂
4. (2 pts) Given an alphabet {a,b,c,d} with respective expected probabilities {.1,.3,.4.,.2}, decode the value .75 as a 8 symbol string.
5. (2 pts) Encoding without scaling.  Redo Example 4.3.5 (which is based on Example 3.2.3), but with underlying probabilites for {a₁, a₂, a₃} of {.7, .1, .2} instead of {.8, .02, .18}.  Submit your answer in binary.
6. (2 pts) Decoding without scaling. Redo Example 4.3.6 with your previous answer (and revised probabilities {.7,.1,.2}).
7. (2 pts) Encoding with scaling.  Redo Examples 4.4.2 also with the revised probabilites of {.7, .1, .2}.
• Submit your answer in binary.
• Only apply scaling rules E₁and E₂, not E₃.
• In example 4.4.2, the first calculation of u⁽³⁾ -  "(0.8 - 0.312)" should say "(0.6 - 0.312)"
8. (2 pts) Decoding with scaling. Redo Example 4.4.3 with your previous answer (and revised probabilities of {.7, .1, .2}).
• Only apply scaling rules E₁and E₂ , not E₃.
• In decoding with scaling, the wordsize technically must be recomputed at each iteration.  For simplicity, use a word size of 6 bits for this problem.
• In example 4.4.3, the first calculation of u⁽³⁾ -  "(0.8 - 0.312)" should say "(0.6 - 0.312)"

Notes

• Students may work individually or in groups of 2.  
• Students in different groups may NOT compare answers prior to submission of their answers. See the syllabus for the full policy on late submissions and academic honesty.