FINALw04_ANS

FINALw04_ANS - 1 McGill University Faculty of Engineering...

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1 McGill University DIGITAL SYSTEM DESIGN Faculty of Engineering ECSE-323B FINAL EXAMINATION WINTER 2004 (April 2004) STUDENT NAME McGILL I.D. NUMBER Examiner: Prof. J. Clark Associate Examiner: Prof. Tal Arbel Signature: Signature: Co-Examiner: Prof. M. Marin Signature: Date: April 21 , 2004 Time: 2:00 pm INSTRUCTIONS: SEE NEXT PAGE.
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2 McGILL UNIVERSITY Department of Electrical and Computer Engineering ECSE-323B Winter 2003 FINAL EXAM Question Maximum Points Points Attained 1 10 2 15 3 20 4 15 5 15 6 15 7 15 8 15 9 15 10 20 11 15 12 10 Total 180 points Please write down your name: _____________________________________ 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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3 Question 1 : CMOS Circuit Technology (10 points) Draw the pull-up and the pull-down networks of a CMOS circuit producing the AND-OR-INVERT function of 4 variables whose Boolean algebraic expression is f (A,B,C,D) = AND-OR-INVERT (A,B,C,D) = NOT[OR[AND(A,B),AND(C,D)]]. Only true variables are available as inputs. Marking scheme : 5 points for the correct pull-up network and 5 points for the correct pull-down network. _________________________________________________________________________________________ ANSWER PULL-UP NETWORK PULL-DOWN NETWORK
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Your Name__________________________________________________________________________________ Question 2 :Boolean Logic Theory (15 points) Draw the circuit producing the function f(A,B,C,D) = Σ m(8,9,10,11,12,13,15) and using ONLY the building block g(x,y,z) = x f8e5 y + x z. Two such blocks are sufficient. (5 points) a) Explain CLEARLY your approach to solve this problem. (5 points) b) Decompose f in terms of g. (5 points) c) Draw the complete minimal circuit. _________________________________________________________________ ANSWER a) We map on a K-map the function f . If f is not a Booean constant (0,1) or one of the input variables or their complement, it must be the output of a building block g. Now we try to express x, y, z as functions of A, B, C, D and determine if these functions are Boolean constants, input variables or their complement. If any of them are not, again, they must be outputs of a bulding block g. We iterate this process until input variables or their complement are found. If g is complete, the process converges. If not, there is no solution. This process is illustrated by the following figure:
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FINALw04_ANS - 1 McGill University Faculty of Engineering...

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