1. [14] From the encoding table as shown below: Symbol A B с D E F G Table 1 Frequency Codeword 40 0 55 100 50 101 70 11

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1. [14] From the encoding table as shown below: Symbol A B с D E F G Table 1 Frequency Codeword 40 0 55 100 50 101 70 1100 11 1101 6 1110 3 1111 a) [3.5] Build the prefix tree according to the Table 1 above. b) [3.5) Use Huffman code to assign new codewords to the symbols (A-G) above. Follow the convention that the group/symbol with higher probability is assigned a '0' and that with lower probability is assigned a 'l'. List out all the codewords in Table 2. Symbol A B с D E F G Table 2 Frequency Codeword (Huffman) 40 55 50 70 11 6 3 c) [2] What is the average codeword length of the original coding (Table 1)? d) [2] What is the average codeword length by using Huffman code (Table 2)? e) [2] What is the minimum average number of bits needed to encode each symbol? ) [1] Using a fixed-length code, what will be the minimum average number of bits needed to encode each symbol?