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?
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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 = 45d + e = 35 + 5 = 40,Now,a + b + c + d + e = 100So,a = 11 = 2 digitsb = 101 = 3 digitsc= 100 = 3 digitsd= 01 = 2 digitse= 00 = 2 digitsAnd,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 digitsi.e.The average code length = 15 × 2 + 25 × 3 + 20 × 3 + 35 × 2 + 5 × 2On solving we get,The average code length = 245Hence 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 herehttps://brainly.com/question/18916556#SPJ4