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dsdmidterm winter 2010

dsdmidterm winter 2010 - Student Name McGILL UNIVERSITY...

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Student Name: Page 1 of 17 McGILL UNIVERSITY Electrical and Computer Engineering Department ECSE-323 DIGITAL SYSTEM DESIGN Winter 2010 MIDTERM EXAM Question Maximum Points Points Attained 1 15 2 10 3 10 4 15 5 20 6 5 Total 75 Please write down your name: __________________________________ Please write your student ID number: ___________________________ ______________________________________________________________ Instructions/Please read carefully! This is a closed 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 yourself accordingly.
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Student Name: Page 2 of 17 Question 1: Boolean Logic Theory (15 marks) Consider the following Boolean function: f(b,d,f,g,e) = bdg+b’dfg+b’d’g+bd’eg. a) Find the minimal SoP form of function f using the Quine-McCluskey method. Clearly state which are the essential prime implicants and prime implicants. b) Perform the factorization of the minimized SoP from part b). Try to get as small a form as possible. c) Perform the decomposition of the minimized function from part b). Solution a) We need to express f in terms of minterms. f(b,d,f,g,e) = bdg+b’dfg+b’d’g+bd’eg = bd(f+f’)g(e+e’) + b’dfg(e+e’) + b’d’(f+f’)g(e+e’) +bd’(f+f’)ge = bdfg(e+e’) + bdf’g(e+e’) + b’dfge + b’dfge’ + b’d’fg(e+e’) + b’d’f’g(e+e’) +bd’fge + bd’f’ge = bdfge + bdfge’ + bdf’ge + bdf’ge’ + b’dfge + b’dfge’ + b’d’fge + b’d’fge’ + b’d’f’ge + b’d’f’ge’ +bd’fge + bd’f’ge = Σ m(11111, 11110, 11011, 11010, 01111, 01110, 00111, 00110, 00011, 00010, 10111, 10011) = Σ m(00010, 00011, 00110, 00111, 01110, 01111, 10011, 10111,11010, 11011, 11110, 11111)
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