hw9sol - (c) E r = {abc, bd, bcd, ad} R t = {abcd} R p = 3)...

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ECE3060: Homework 9 Solutions 1) (a) C = a’d’ + cd + ad + bc’d’ (b) a’d’ cannot be reduced cd can be reduced to a’cd ad can be reduced to ac’d bc’d’ can be reduced to abc’d’ (c) C is irredundant, prime, and minimum with respect to single implicant containment. (d) E r = {a’d’, cd, ad, bc’d’} R t = Ø R p = Ø 2) (a) a’b’c can be reduced to a’b’cd b’d’ cannot be reduced abcd cannot be reduced bc’d can be reduced to a’bc’d ad can be reduced to ab’d (b) F is redundant (because of abcd) not prime (because of abcd) not minimum with respect to single implicant containment (because of abcd)
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Unformatted text preview: (c) E r = {abc, bd, bcd, ad} R t = {abcd} R p = 3) x = cd + ac + abed + bc + abc x/a = bed + bc n.c.f. x/a= c n.c.f. x/b = aed + ac n.c.f. x/b= c n.c.f. x/c = d + a + b + ab kernel x/d = abe + c kernel x/e = abd n.c.f. x/ab = ed + c kernel Kern(x) = {d + a + b + ab, abe + c, ed + c, x} y = ab + acd + bd + ad + abe y/a = cd + be kernel y/a= b + d kernel y/b = a n.c.f. y/b= d + ae kernel y/c = ad n.c.f. y/d = ac + b + a kernel y/e = ab n.c.f. Kern(y) = { cd + be, b + d, d + ae, ac + b + a, y} Largest common sub-expression a + b...
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This note was uploaded on 02/19/2010 for the course ECE 3060 taught by Professor Shimmel during the Spring '07 term at Georgia Institute of Technology.

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hw9sol - (c) E r = {abc, bd, bcd, ad} R t = {abcd} R p = 3)...

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