hw1soln - by 10b twice = b + a.c by 12b = a.c + b = RHS by...

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HW#1 Solutions 1/23/2009 1. (a) (b) (c) f = x 2. (a) F = (A.B)’.(A.B + B.C) (b) A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 3. (a) F = x’.y (b) Lecture 4 1. (a) A b c (a+b).a’ + c.b (a’+c).b 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 (b) LHS = (a+b).a’ + c.b = a’.(a+b) + c.b by 10a = a’.((a’)’+b) + c.b by 9 = a’.b + c.b by 16b = b.a’ + b.c by 10a twice = b.(a’ + c) by 12a = (a’ + c).b = RHS by 10a x y f 0 0 0 0 1 0 1 0 1 1 1 1
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(c) The dual theorem is: (a.b +a’).(c+b) = a’.c + b LHS = (a.b +a’).(c+b) = (a’ + a.b).(c+b) by 10b = (a’ + (a’)’.b).(c+b) by 9 = (a’ + b).(c+b) by 16a = (b + a’).(b+c)
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Unformatted text preview: by 10b twice = b + a.c by 12b = a.c + b = RHS by 10b 2. (a) (b) Cost = # gates + # inputs = 9 + 23 = 32 (c) (Note that some obvious steps are skipped in the following.) f = (abc + abc) + (abc + abc) + (abc + abc) duplicating abc by 7b = ab + ac + ac by 14a three times = ab + c by 14a again (d) (e) Cost = 3 + 5 = 8...
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hw1soln - by 10b twice = b + a.c by 12b = a.c + b = RHS by...

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