$3.$ Since the entropy value calculated in part $2$ is less than $4$ bits, it means that you can find more efficient code strings for values $0,1,2,..,15$ using the Huffman coding. Huffman coding is an algorithm used to compress data without losing any information. It assigns shorter codes to more$-$frequent $($more likely$)$ values and longer codes to less$-$frequent $($less likely$)$ values. The following video illustrates how Huffman algorithm works. This algorithm assigns codes to different values by constructing a tree called Huffman tree:

Assuming that the following tree is drawn using the Huffman algorithm, find the code string for every value from $0$ to $15.$ Also, calculate the average number of bits for each value. Is the average number of bits similar to the number that you calculated in part $2?$

ChatGPT