$.$ Huffman Encoding

Color Frequency

a $5$

b $11$

c $2$

d $2$

e $1$

f $3$

g $9$

h $4$

i $2$

j $1$

k $1$

l $6$

a$.$ Create a Huffman tree from the colors and frequencies above.

b$.$ Determine the new code to accompany each color.

c$.$ Compute how many bits were in the original image?

d$.$ Compute how many bits are in the encoded image?

e$.$ If you had the Huffman tree for decoding, how would you decode the string of bits?

f$.$ Rather than save the whole Huffman tree in the encoded file, it's possible to save just the frequency table. Why is this sufficient?

g$.$ Assume that the encoded file contains the compressed image file and also the frequency table, what is the compression rate of the image after the Huffman encoding? $($You don't have to consider the size of the file header.$)$

h$.$ Is Huffman encoding lossy or lossless? Explain what this means.