Consider a source with symbols A, B, C, D with probabilities 1/2, 1/4, 1/8, and 1/8 respectively. What is the average number of bits per symbol for the…
Consider a source with symbols A, B, C, D with probabilities 1/2, 1/4, 1/8, and 1/8 respectively. What is the average number of bits per symbol for the Huffman code generated from above information?
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Correct answer: (B) 1.75 bits per symbol
Explanation
Huffman code lengths: A (1/2) → 1 bit, B (1/4) → 2 bits, C (1/8) → 3 bits, D (1/8) → 3 bits. Average length = (1/2 × 1) + (1/4 × 2) + (1/8 × 3) + (1/8 × 3) = 14/8 = 1.75 bits per symbol.