Consider the following tree for a prefix code:

A text file contains only characters from the set {a, b, c, d, e, f}. The frequency of each letter in the file is:

a: 5%

b: 5%

c: 10%

d: 15%

e: 25%

f: 40%

(a)

What is the average number of bits per character used in encoding the file?

(b)

Is there a prefix tree for the set {a, b, c, d, e, f} that would result in fewer bits per character on average for the given frequencies of the characters?

1 0 0 0 1 0