Question $3$

Kate wants to send a very long message to Mike. Kate notices that some letters in the message appear

more frequently than others. Thus, she wants to encode the message and then send the encoded message

to Mike. Mike also receives a "key" $($code$)$ from Kate to decode the received encoded$-$message. Assume

that the message Kate sent has the following characters appearing with their corresponding frequencies,

as shown in the table below. Construct a Huffman Tree for the given data in the table and show the

final Huffman code for each character. Note: when assigning codes in the tree, assign the left child as $0$

and the right child as $1.$ Also, calculate the average number of bits needed to encode a character $($use

appropriate units$).$