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hw9sol - (c E r ={a’b’c b’d’ bc’d ad R t ={abcd R...

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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 = {a’b’c, b’d’, bc’d, ad} R t = {abcd} R p = Ø 3) x = cd + a’c + abed + b’c + 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 = a’b + acd + b’d + a’d + ab’e y/a = cd + b’e 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 + b’e, b + d, d + ae, ac + b’ + a’, y} Largest common sub-expression a’ + b’...
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  • Spring '07
  • Shimmel
  • Trigraph, Initialisms, ABC Television, single implicant containment, kernel n.c.f. kernel, kernel kernel n.c.f.

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