A discrete memoryless information source is described by the alphabet x = {x1, x2,

x3, x4, X5, X6) with probabilities (1/32, 1/8, 1/2, 1/16, 1/32, 1/4), respectively.

1. Design a Huffman code for this source and determine the average code word

length of the Huffman code.

2. Can you improve the Huffman code by encoding the second extension of this

source (in other words, using two letters at a time and designing the Huffman

code for that source)? Why?

3. Is there any way to improve the performance of the Huffman code designed in

Part 1? (By improving the performance, we mean designing a code with a lower

average code word length.)