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

   https://brainly.com/question/18916556

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