$1.[10]$ From the encoding table as shown below:

Symbol Frequency Codeword

A $1050$

B $50100$

C $65101$

D $601100$

E $111101$

F $61110$

G $31111$

Table $1$

a$)[1]$ Build the prefix tree according to the Table $1$ above.

b$)[3\mathrm{.}5]$ 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 $1.$ List out all the codewords in

Table $2.$