MIDF06_ANS_revised

MIDF06_ANS_revised - ECSE-323 Department of Electrical and...

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McGILL UNIVERSITY Department of Electrical and Computer Engineering ECSE-323 Fall 2006 MIDTERM EXAM Question Maximum Points Points Attained 1 10 2 10 3 15 4 15 5 15 6 10 Total 75 points Please write down your name: ANSWER KEY Please write your student ID: ______________________________________ Instructions/Please read carefully! This is a close book exam. 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 yourself accordingly. Your Name_______________________________________________________
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Question 1 :Boolean Logic Theory (10 points) (5 points) a) Produce the Shannon expansion of F with respect to variables A and C. F(A,B,C,D) = A B + f8e5 C f8e5 B + D f8e5 A + f8e5 B f8e5 D + A C. (5 points) b) Using DUALITY convert the following sum-of-products expression into its product-of-sums equivalent . F(A,B,C,D) = A f8e5 D f8e5 C + B A D + f8e5 A C D + f8e5 B C D. ___________________________________________________________________________ ANSWER: a) F(A,B,C,D) = f8e5 A f8e5 C [F(0,B,0,D)] + f8e5 A C [F(0,B,1,D)] + A f8e5 C [F(1,B,0,D)] + A C [F(1,B,1,D)]. F(A,B,C,D) = f8e5 A f8e5 C [ f8e5 B + D + f8e5 B f8e5 D ] + f8e5 A C [ D + f8e5 B f8e5 D ]+ A f8e5 C [B + f8e5 B + f8e5 B f8e5 D ] + A C [1]. F(A,B,C,D) = f8e5 A f8e5 C [ f8e5 B + D] + f8e5 A C [ f8e5 B + D ]+ A f8e5 C [1 ] + A C [1]. b) F Dual = (A + f8e5 D + f8e5 C)( B + A + D)( f8e5 A + C + D)( f8e5 B + C + D). F Dual = (AB + A + AD + f8e5 DB + f8e5 DA + f8e5 CB + f8e5 CA+ f8e5 CD)( f8e5 A f8e5 B + f8e5 AC+ f8e5 AD+ C f8e5 B+ C + CD + D f8e5 B + DC + D). Simplifying terms within each parenthesis (applying xy + x = x), we obtain F Dual = (A + f8e5 DB + f8e5 CB + f8e5 CD)( f8e5 A f8e5 B + C + D). Expanding
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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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MIDF06_ANS_revised - ECSE-323 Department of Electrical and...

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