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fa10_hw2 Solution

# fa10_hw2 Solution - CS231 Fall 2010 Homework 2 Solution...

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CS231 Fall 2010 Homework 2 Solution 1. (20 pts) Use K-maps to simplify the following Boolean functions: a. F( X, Y, Z ) = XY' + X'Y + X'Z + Y'Z' F = X' + Y' b. F( A, B, C, D ) = ACD + A'BC + BD' + BC'D F = B + ACD c. F( A, B, C, D ) = AB'C + A'B'C' + A'BC'D + B'CD' + C'D' F = AB'C + A'C' + C'D' + B'D' d. F( X, Y, Z ) = ΠM( 0, 2, 3, 5 ) = Σm( 1, 4, 6, 7 )

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F = XY + XZ' + X'Y'Z e. F( A, B, C, D ) = Σm( 2, 4, 5, 6, 7, 9, 10, 11, 14 ) F = A'B + CD' + AB'D
2. (10 pts) The following K-maps all attempt to show the function F with don't-care conditions d a. Which K-maps have invalid groupings? Explain. A: Improper grouping (blue). The 1 s can only be wrapped around if they are in the same column in the outmost blocks. B: Has a zero D: Has a grouping that is not a power of 2

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b. What is the minimum sum of products of function F? F = X'Y'Z + WX'Z + YZ' + XZ' (as shown in Figure c) OR F= X'Y'Z + WX'Y + YZ' + XZ' (when the 1 in the pink rectangle is grouped with the one on its right, instead of the X) 3. (12 pts) Use K-map to obtain a minimal sum of products (MSP) and a minimal product of sums (MPS) of the following function. ("d" means don't care.) F(W,X,Y,Z) = ∑ m(0,1,2,4,7,8,13) d(W,X,Y,Z) = ∑ m(5 ) (a) minimal sum of products (MSP) F(W,X,Y,Z) = W'Y'+ W'X'Z' + W'XZ + XY'Z + X'Y'Z'
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