MIDTERMw05-ANS

MIDTERMw05-ANS - ECSE-323 Electrical and Computer...

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McGILL UNIVERSITY Electrical and Computer Engineering Department ECSE-323 Winter 2005 MIDTERM EXAM Question Maximum Points Points Attained 1 10 2 15 3 20 4 20 5 10 Total 75 points ANSWER KEY Please write down your name: _____________________________________ Please write your student ID: ______________________________________ Instructions/Please read carefully! This is a close book quiz. No books or notes are allowed. You may use a standard calculator. All work is to be done on the attached sheets and under no circumstance are booklets or loose sheets to be used. Write your name at the top of every sheet. Read the question carefully. If something appears ambiguous, write down your assumption. The points have been assigned according to the formula that 1 point = 1 exam minute, so please pace your self accordingly.
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Question 1 :Boolean Logic Theory (10 points) (5 points) a) Find P and Q such that A C + B f8e5 C + f8e5 B f8e5 C D = B P + f8e5 B Q. (5 points) b) Find X and Y such that A C + B f8e5 C + f8e5 B f8e5 C D = (A + X) ( f8e5 A + Y). NOTE: To obtain full mark it is mandatory to explain clearly the steps followed. ____________________________________________________ _ ANSWER a) The Shannon Expansion with respect to B gives: B [AC + f8e5 C] + f8e5 B [AC + f8e5 C D]. Thus P = [AC + f8e5 C] and Q = [AC + f8e5 C D. b) Using the K-map of F , we find the expression for f8e5 F f8e5 F = f8e5 AC + f8e5 B f8e5 C f8e5 D. Expanding f8e5 F with respect to A, we obtain f8e5 F = f8e5 A [C + f8e5 B f8e5 C f8e5 D] + A [ f8e5 B f8e5 C f8e5 D ]. Using the DeMorgan’s Theorem on f8e5 F ,we obtain: ____________ ________ F = (A + [C + f8e5 B f8e5 C f8e5 D] ) ( f8e5 A + [ f8e5 B f8e5 C f8e5 D ] ), which is of the form (A + X ) ( f8e5 A + Y). Thus: X = f8e5 C B + f8e5 C D and Y = B + C + D. 2
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Question 2 : CMOS Circuit Technology (15 points) Consider the function of 4 variables F(A,B,C,D) = Σ m (3,5,6,7,9,10,11,12,13,14,15). Design a CMOS circuit that produces the function
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This note was uploaded on 11/22/2010 for the course ECSE ecse 323 taught by Professor Redacka during the Winter '07 term at McGill.

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MIDTERMw05-ANS - ECSE-323 Electrical and Computer...

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