hw3_solution_new

# hw3_solution_new - Homework#3 due February 1 at noon ECE...

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Homework #3 due February 1 at noon ECE 15a Winter 2010 1. Express each of the following functions in disjunctive normal form (DNF) in the smallest possible number of variables: a) f=(u’+w’v)’(uv+w)’ = (u’+w’v+uv+w)’ = (u’+w+v)’ = uw’v’ b) g=xy’z’+(x+y’)(x+z’) = xy’z’+x+y’z’ =x+y’z’ =x’y’z’+xy’z’+xy’z+xyz’+xyz c) h=(x+z’)(x’+y)(x’+z’) = (x+z’)(x’+z’)(x’+y) =z’(x’+y) =x’y’z’+x’yz’+xyz’ 2. Write each of the following functions in DNF in three variables x,y,z. Express your results using the m-notation. Assume (x,y,z)=(0,0,1) denotes m=1; a) f= (x’+y’)’ = xy = xyz+xyz’ = ∑ mሺ6,7ሻ b) g=xz’+x’z =xyz’+xy’z’+x’yz+x’y’z = ∑ mሺ1,3,4,6ሻ 3. The function f(x,y,z) is 1 if either x = 1 and y=z=0, or if z=0 and y=1; and is 0 otherwise. a) Construct truth table for f(x,y,z). (2p) (x,y,z) f(x,y,z) (x,y,z) f(x,y,z) 000 0 100 1 001 0 101 0 010 1 110 1 011 0 111 0 b) Express f using the M-notation. (2p)

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hw3_solution_new - Homework#3 due February 1 at noon ECE...

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