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Unformatted text preview: ECE 110
Professors Brunet and Trick November 14, 2005 HOUR EXAMINATION #3
LAST Name (use capital letters):
First Name (use capital letters): t
Signature: Circle your section: AL1(3pm)Trick BL1(1pm)Brunet DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD 

—


_ A. Write or print clearly. Answer each problem on the exam itself. If you
need extra paper, there is an extra sheet at the end of this exam. Clearly
identify the problem number on any additional pages. The ASCII COde, the
Morse Code alphabet, the UPC code, numbers and properties for log base 2
are given at the end of the exam. B. In order to receive partial or full credit, you must show all your work,
e. g., your solution process, the equation(s) that you use, the values of the
variables used in the equation(s), etc. You must also include the unit of measurement in each answer. Students caught cheating on this exam will earn a grade of F for the
entire course. Other penalties may include suspension and/or dismissal
from the university. Problem 1 (20 points) O
l
I
l Fill in the followingotableo for consecutivecfock pulses. Problem 2 (20 points) Check the most appropriate answer for all questions below. 33¢)”:
21m Qo F<A<B> mo 3 1.1 o 31.1 down 3) counter 21m
>C comparator = G (A = B) F . I o 6 o [
clock H (A '> B) Period 7" 47— The duty cycle of F is: [j 0% E 25% El 33% I:] none of the previous The period of G is: I] T E] 2T El 3T MHOHC of the previous
T is the clock period. b) . After 2 clock pulses (at t = 2)
3blt the re ister contains
shift register g '
m 101 D 011
1:] 000 E} 111 E] none of the previous Problem 3 (20 points) A wheel has 3 evenly spaced spokes. Each spoke is of a
different color (see ﬁgure). The wheel is rotating at a rate of f = 12 revolutions per second. Show work of a_ll parts.
Red Green a) If the wheel is ﬁlmed at a sampling frequency fS = 36 frames per second, is there aliasing? E] YES END
4‘, > I! 2 24/42 Draw the ﬁrst frame seen after t = Os; indicate time, too. b) For what sampling frequency would the wheel seem immobile? (Give the largest
number possible.) .L ..
IW Av #151750 “F5 ’ [lyvéa c) For what ranges of sampling frequencies would the wheel seem to be going
backward? (Give largest numbers possible.) '8 . 2 {go/J.” : /.2/7(7_z £5 > 27/{1' 1w air‘afﬁr Problem 4 (20 points) a) (1 0 pts. ) Information is encoded in the 7bit ASCII code. In transmission tests it is
discovered that on the average a single bit error occurs in every few hundred
characters received. A decision is made to add the capability to detect and correct
Single bit errors. Two schemes are proposed: [a] send the message in triplicate, or [b]
add an even parity bit to the code for each character and, for every block of 10
characters to be transmitted, add a redundanc check code word in order to correct any single error that is detected. Compute the compression ratio and savings if
Scheme [b] is used instead of Scheme [a]. a) 3t at 7&7 chjgr = 2/0 W/b/mk V Hack é) ’5' (Ofl>ch%/ukt [vul‘ 3 ‘L I ' /o . ,2/9 —W .
Rcompression = :52. SaVlng‘S = 37—2— = u a , .‘ b) (1 Opts.) The relative frequency for a message consisting of the following six symbols
is A = 1/3, B = 5/24, C = l/6, D = l/6, E = 1/12, F = 1/24. The Huffman code for these symbols is A(1 1), B(Ol), C(00), D(lOl), E(1001),F(1000). Compute the
average code length, and the savings achieved over the minimum ﬁxed length code. " 2x1. 3L 1, _L
6 1* Ké+<fx +sz 5
@ “K”? Wait“ a
': ,(o 'f’lO‘l’X +11%”? =£&: \ z 3 ’ ‘
Ft'xed (04¢. ZééW <1] 40 K A la '7’ 41
Kc _ A; \ \ Lavg— 02.42, 5):ng , Savings: X/Qﬂo: omp' Problem 5 (20 points) A secret 16bit binary key was used to encrypt a message encoded in the ASCII code.
The key was generated using the PRNG X(n + 1) = [A * X(n) + B]modN
where A = 7, B = 11, and N = 16. The secret seed X(O) = 5 was used to generate a 16bit
key from the sequence X(O), X(l), X(2), X(3), X(O), repeats. Your job is to decode
the encrypted message and convert it back to ASCII characters. a) (8 pts.) First, given X(O) = 5, X( 1) = 14, X(2) = 13, compute X(3). X0, xi, )4), X3] X0) Kt)” c...
5,741) )5, 4/ 53 Nil/1%. X3=
Mud, 456/WW 05x54“, H b) (12 pts.) Use this key and the XOR operation to decrypt the encrypted message and
convert to ASCII characters. encrypted .mma+II!!!IIIIIIlllllllllllllﬂlﬂllllllﬂl
. Ei an In la la la uaiEmIE I
kw+Emaiiunﬁimuﬂﬁnnﬂﬁmaﬂﬂnmainut ulnonE dwwekIliaIHHE!EllﬁlﬂllilliilﬁllﬁﬂﬁllHill
message I I
D C C 3
Message = 44/ ‘Dea £0!” ‘éZtvce,
_ XoK +4
owe, H ...
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