Solve the following problem:
A DMS has an alphabet of eight letters xi, 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.