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ECE320
Makeup Second Examination
Spring 2006
Cornell University
T.L.Fine
CLOSED BOOK, NO NOTES, CALCULATORS, OR SCRAP PAPER. TURN OFF CELLPHONES.
ALLOTTED TIME IS 1 hour and 30 min.
SHOW YOUR WORK, GIVE REASONS, NOT JUST ANSWERS.
Place your threedigit ID number, not your name, on each sheet.
Work each problem on a separate sheet of paper so that the
individual questions can be separated for grading.
1. Consider a source with ﬁve symbols
[a,b,c,d,e]
having correspond
ing probabilities of being chosen of
p
= [1
,
1
,
2
,
4
,
8]
/
16. Consider a
preﬁx code for this set of symbols with the corresponding codewords being
[0000
,
0001
,
001
,
01
,
1].
(a)(2pts) What is the expected codeword length?
(b)(3pts) Calculate the source entropy
H
in bits.
(c)(4pts) Construct a Huﬀman code for this source, evaluate its expected
length, and compare it to the entropy found in (b).
(d)(6pts) Consider the set of codewords [00
,
01
,
10
,
11
,
1] for the symbols
listed in (a). Evaluate the expected codeword length and compare it to the
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This note was uploaded on 04/14/2008 for the course ECE 3200 taught by Professor Fine during the Spring '06 term at Cornell University (Engineering School).
 Spring '06
 FINE

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