MIDw06_ANS

# MIDw06_ANS - ECSE-323 Department of Electrical and Computer Engineering Winter 2006 McGILL UNIVERSITY MIDTERM EXAM Question 1 2 3 4 5 6 Total

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McGILL UNIVERSITY Department of Electrical and Computer Engineering ECSE-323 Winter 2006 MIDTERM EXAM Question Maximum Points Points Attained 1 10 2 10 3 15 4 15 5 10 6 15 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) Using the Quine-McCluskey method, find ALL minimal two-level sum-of-products expressions of the function F (A,B,C,D) = Σm(0,4,5,8,10,13,14,15). (5 points) a) Give the list of all prime implicants of F (5 points) b) Using the PETRICK FUNCTION, find ALL MINIMAL two-level sum-of- products expressions of F . ___________________________________________________________________________ ANSWER First Reduction No further reduction List of Prime implicants ID A B C D 0 0 0 0 0 4 8 0 1 0 0 1 0 0 0 5 10 0 1 0 1 1 0 1 0 13 14 1 1 0 1 1 1 1 0 15 1 1 1 1 Covering Table | <--------------------minterms ---------------------------------->| P.I. Group 0 4 5 8 10 13 14 15 P1 0,4 f8e5 A f8e5 C f8e5 D P2 0,8 f8e5 B f8e5 C f8e5 D P3 4,5 f8e5 A B f8e5 C P4 8,10 A f8e5 B f8e5 D P5 5,13 B f8e5 C D f8e5 A f8e5 C f8e5 D f8e5 B f8e5 C f8e5 D f8e5 A B f8e5 C A f8e5 B f8e5 D B f8e5 C D A C f8e5 D A B f8e5 D A B C ID A B C D 0,4 0 - 0 0 0,8 - 0 0 0 4,5 0 1 0 - 8,10 1 0 - 0 5,13 - 1 0 1 10,1 4 1 - 1 0 13,1 5 1 1 - 0 14,1 5 1 1 1 -
P6 10,14 A C f8e5 D P7 13,15 A B f8e5 D P8 14,15 A B C Your Name_______________________________________________________ Question 1 :Boolean Logic Theory (10 points) (Continues) There are no essential prime implicants and no reduction of the covering table is possible. The Petrick function should give us the minimal forms.

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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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MIDw06_ANS - ECSE-323 Department of Electrical and Computer Engineering Winter 2006 McGILL UNIVERSITY MIDTERM EXAM Question 1 2 3 4 5 6 Total

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