Consider the following two Huffiman decoding trees for a variable-length code involving 5 symbols: A, B, C, D and E Tree #1 Tree #2 I 0 A BC 0 1 B CD E D E A. Using Tree #1, decode the following encoded message: "01000111101". B. Suppose we were encoding messages with the following probabilities for each of the 5 symbols (A)- 0,5. p(B)-p(C)-p(D)-p(E)-0.125. Which of the two encodings above (Tree #1 or Tree #2) would yield the shortest encoded messages averaged over many messages? C. Using the probabilities of part (B), if you learn that the first symbol in a message is "B", how many bits of information have you received? 4 0

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Q1/ Consider the following two Huffinan decoding trees for a variable-length code involving 5 symbols: A, B, C, D
and I.
Tree #1
Tree #2
1
0
A
BC
1
B
C D
E
DE
A. Using Tree #1, decode the following encoded message: "01000111101".
B. Suppose we were encoding messages with the following probabilities for each of the 5 symbols (A)-
0.5.p(B)-p(C)-p(D)-p(E)-0.125. Which of the two encodings above (Tree #1 or Tree #2) would
yield the shortest encoded messages averaged over many messages?
C. Using the probabilities of part (B), if you learn that the first symbol in a message is "B", how many bits
of information have you received?
D. Using the probabilities of part (B), If Tree #2 is used to encode messages what is the average length of
100-symbol messages, averaged over many messages?
Transcribed Image Text:Q1/ Consider the following two Huffinan decoding trees for a variable-length code involving 5 symbols: A, B, C, D and I. Tree #1 Tree #2 1 0 A BC 1 B C D E DE A. Using Tree #1, decode the following encoded message: "01000111101". B. Suppose we were encoding messages with the following probabilities for each of the 5 symbols (A)- 0.5.p(B)-p(C)-p(D)-p(E)-0.125. Which of the two encodings above (Tree #1 or Tree #2) would yield the shortest encoded messages averaged over many messages? C. Using the probabilities of part (B), if you learn that the first symbol in a message is "B", how many bits of information have you received? D. Using the probabilities of part (B), If Tree #2 is used to encode messages what is the average length of 100-symbol messages, averaged over many messages?
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