A series of messages is to be transferred between two computers over a PSTN$.$ The

messages comprise just the characters A through $H.$ Analysis has shown that the

probability $($relative frequency of occurrence$)$ of each character is as follows:

$A=0\mathrm{.}3,B=0\mathrm{.}2,C$ and $D=0\mathrm{.}14,E,F,G,$ and $H=0\mathrm{.}055$

Use Shannon's formula to derive the minimum average number of bits per

character

Use Huffman coding to derive a codeword set and prove that this is the minimum

set by constructing the corresponding Huffman code tree

Derive the average number of bits per character for your codeword set and

compare this with:

The entropy of the messages $($Shannon$\text{'}$s value$),$

Fixed$-$length binary codewords,

$7-$bit ASCII codewords