The average length encoding of a letter for a Huffman code of the letters and their given frequencies will be 245.
We have,
Frequencies:
a = 0.15 = 15,
b = 0.25 = 25,
c = 0.20 = 20,
d = 0.35 = 35,
e = 0.05 = 5,
So,
Now,
According to the question,
We will make Huffman tree,
i.e.
a = 0.15 = 15,
b + c = 25 + 20 = 45
d + e = 35 + 5 = 40,
Now,
a + b + c + d + e = 100
So,
a = 11 = 2 digits
b = 101 = 3 digits
c= 100 = 3 digits
d= 01 = 2 digits
e= 00 = 2 digits
And,
We know that,
Total bits required to represent Huffman code = 12.
So,
Now,
The average code length = a * 2 digits + b * 3 digits + c * 3 digits + d * 2 digits + e * 2 digits
i.e.
The average code length = 15 × 2 + 25 × 3 + 20 × 3 + 35 × 2 + 5 × 2
On solving we get,
The average code length = 245
Hence we can say that the average length encoding of a letter for a Huffman code of the letters and their given frequencies will be 245.
Learn more about Huffman code here
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