Determine a ternary code by huffman encoding procedure

Question

Response to the following problem:

A DMS has an alphabet of eight letters x_i, i = 1, 2,..., 8, with probabilities given in Problem 1. Use the Huffman encoding procedure to determine a ternary code (using symbols 0, 1, and 2) for encoding the source output.

Problem 1:

A DMS has an alphabet of eight letters x_i, i = 1, 2,..., 8, with probabilities 0.25, 0.20, 0.15, 0.12, 0.10, 0.08, 0.05, and 0.05.

1. Use the Huffman encoding procedure to determine a binary code for the source output.

2. Determine the average number R of binary digits per source letter.

3. Determine the entropy of the source and compare it with R.