Test by Bikram | Mock GATE | Test 3 | Question: 35

Question

Consider the following set of messages with their frequencies:
 $$\begin{array}{|c|c|c|} \hline \textbf{Message} & \textbf{Frequency}  \\ \hline A & 50\: \text{million}  \\ \hline B & 10\: \text{million}   \\ \hline C& 24\: \text{million} \\ \hline  D & 36\: \text{million}   \\ \hline \end{array}$$

The percentage improvement for total binary stream transmission using Huffman Encoding over simple encoding is _______ %.

Comments

Normaly we would need (50+10+24+36)*2 = 240 bits

After huffman,

we would need (1*50+3*10+3*24+2*36) = 224 bits

improvement % = (240-224)/240 *100 = 6.66%

why is the ans 5 % ?

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the answer should be 6.6666%

Answer 1

In simple encoding  (50+10+24+36)*2 = 240 bits

After Huffman encoding ,

 (1*50+3*10+3*24+2*36) = 224 bits

%  improvement  is = (240-224)/240 *100 = 6.66%

Comments

@Bikram sir,

In simple encoding, on what basis and how u r multiplying with 2???

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Two bits required to represent each message type.