ch 3 Marcovitz_Ch3_Solutions_Fall2011

ch 3 Marcovitz_Ch3_Solutions_Fall2011 - EC262 Digital...

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1 EC262 Digital Systems Fall 2011 Chapter 3 Solutions Textbook: Marcovitz, Introduction to Logic Design , 3 rd ed. Exercise 1 (ae), Exercise 2(abcdhj), Exercise 3 (a), Exercise 5 (d and e), Exercise 7 (a and e), Exercise 9 (a), Exercise 11 (c and f). Exercise 1 : Plot the following functions on the K-map. a. f(a,b,c) = Σ m(1,2,3,4,6) ab c 00 01 11 10 0 1 1 1 1 1 1 e. h = x + yz' + x' z xy z 00 01 11 10 0 1 1 1 1 1 1 1 1 Exercise 2 : Find all the minimum SOP expressions. a. f(a,b,c) = Σ m(1,2,3,6,7) ab c 00 01 11 10 0 1 1 1 1 1 1 f = b + a'c b. g(w, x, y) = Σ m(0,1,5,6,7) (2 solutions) Solution 1: wx y 00 01 11 10 0 1 1 1 1 1 1 f = wy + wx + w'x' Solution 2: wx y 00 01 11 10 0 1 1 1 1 1 1 f = x'y + wx + w'x'
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2 c. h(a, b, c) = Σ m(0,1,2, 5,6,7) (2 solutions) Solution 1: ab c 00 01 11 10 0 1 1 1 1 1 1 1 f = bc' + ac + a'b' Solution 2: ab c 00 01 11 10 0 1 1 1 1 1 1 1 f = b'c + ab + a'c' d. f(a,b,c,d) = Σ m(1,2,3,5,6,7,8,11,13,15) ab cd 00 01 11 10 00 1 01 1 1 1 11 1 1 1 1 10 1 1 f = ab'c'd' + a'd + bd + a'c + cd h. g(w,x,y,z) = Σ m(2,3,6,7,8,10,11,12,13,15) (2 solutions) Solution 1: wx yz 00 01 11 10 00 1 1 01 1 11 1 1 1 1 10 1 1 1 g = w'y + yz + wxy' + wx'z' Solution 2: wx yz 00 01 11 10 00 1 1 01 1 11 1 1 1 1 10 1 1 1 g = w'y + wy'z' + wxz + x'y
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3 j. F(W,X,Y,Z) = Σ m(0,2,3,4,5,8,10,11,12,13,14,15)
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ch 3 Marcovitz_Ch3_Solutions_Fall2011 - EC262 Digital...

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