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# hw9 - F F a,b,c,d = a b c b d abcd bc d ad(a For each...

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ECE3060: VLSI and Advanced Digital Design Fall 2007 Homework #9: due November 12 Use the expression format for answering 1(a), 1(d), and 2(c), e.g., C = ab 0 + c . 1. Consider the following binary function: F ( a,b,c,d ) = X (0 , 2 , 3 , 4 , 6 , 7 , 9 , 11 , 12 , 13 , 15) (a) Find an initial cover C using the Expand operation. Use the following rules: visit minterms in the order they appear in F . expand variables under the ordering [ c,a,b,d ]. (b) For each implicant in C , indicate if it is reducible. If so, give the expression for the reduced implicant, e.g., “ ab 0 can be reduced to ab 0 c 0 ”. You are to examine reducibility only—do not commit your change on C . (c) Is C irredundant? Is it prime? Is it minimum with respect to single implicant containment? (d) Perform the Irredundant operation on C to ﬁnd a minimal cover M . Indicate the corresponding E r , R t , and R p sets. 2. Consider the following binary function (do not simplify
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Unformatted text preview: F ): F ( a,b,c,d ) = a b c + b d + abcd + bc d + ad (a) For each implicant in F , indicate if it is reducible. If so, give the expression for the reduced implicant, e.g., “ ab can be reduced to ab c ”. You are to examine reducibility only—do not commit your change on F . (b) Is F irredundant? Is it prime? Is it minimum with respect to single implicant containment? (c) Perform the Irredundant operation on F to ﬁnd a minimal cover M . Indicate the corresponding E r , R t , and R p sets. 3. Find the kernel set for x = cd + a c + abed + b c + abc y = a b + acd + b d + a d + ab e What is the largest common sub-expression that can be extracted from x and y ? cube sheet (origin is located at the lower/left/front corner of the inner-cube) (b) (a) (c)...
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