ex3ans - The Chinese University of Hong Kong Department of...

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Unformatted text preview: The Chinese University of Hong Kong Department of Computer Science and Engineering ERG2020A (Fall 2007): Revision Exercise # 3 Suggested Solution 1. Determine a min. SOP expression for [5 pts] f(a,b,c,d,e) = ( a + c + d)( a + b + e)(a + c + e )(c + d + e )(b + c + d + e)( a + b + c + e ) f = ( a + c + d )( a + b + e )( a + c + e )( c + d + e )( b + c + d + e )( a + b + c + e ) = a c d + a b e + a ce + c d e + b c d e + ab c e e e c d a b 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 f = a d e + bd e + a c de + a c e + abc + ace + a b de 2. Plot the following function on a K-map and [6 pts] F(A,B,C,D) = B C + A BD + ABC D + B C (a) find the min. SOP A C B 1 D 1 1 1 1 1 1 1 1 1 1 min. SOP: F = B + A D + AC D 1 (b) find the min. POS A C B D 1 1 1 1 1 F = ABD + A B D + AB C min. POS: F = ( A + B + D )(A + B + D)( A + B + C) 3. Find the min. SOP for each function [10 pts] (a) f(a,b,c,d) = ∑ m (0 , 1 , 5 , 8 , 12 , 14 , 15) + ∑ d (2 , 7 , 11) A D C B 1 1 1 1 1 1 1 X X X min. SOP: f = a b c + abc + a c d + a c d (b) f(a,b,c,d) = Q M (0 , 1 , 4 , 5 , 10 , 11 , 12) · Q D (3 , 8 , 14) f = ∑ m (0 , 1 , 4 , 5 , 10 , 11 , 12) + ∑ d (3 , 8 , 14) (Because m i = M i ) A D C B 1 1 1 1 1 X X 1 X min. SOP: f = a c + bc + a c d 2 4. Give all PI’s, Essential points, EPI’s and a min. cover [5 pts] C B A 1 D 1 1 1 1 1 1 1 all PI’s: B D , A C D , BCD, ACD, A B C Essential points:...
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ex3ans - The Chinese University of Hong Kong Department of...

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