A file containing the following characters needs to be compressed: $A(10),B(15),C(30),D(5),E(20),F(40),$ and $G(10),$ where the numbers in parentheses represent the frequency of each cheracter.

a$)$ By considering the minimum number of bits required to represent the distinct characters, assign a fixed$-$length binary encoding to each character. Eyplain how you derived the fixed$-$length code. $(2$ points$)$

b$)$ Use the Huffman coding greedy approach to generate variable$-$length codes for each character. Show all steps, including the construction of the Huffman tree and the derivation of the variablelength codes. $(15$ points$)$

c$)$ Calculate the total number of bits required to encode the fille using both fixed$-$length encoding and variable$-$length encoding. $(3$ points$)$

d$)$ Calculate the compression ratio achizved by using Huffman encoding compared to fixed$-$length encoding. $(5$ points$)$