Question

What is the average length encoding of a letter for a huffman code of these letters and their frequencies: a : 0.15, b : 0.25, c : 0.20, d : 0.35, e : 0.05?

Answers

  1. 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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