Homework 3 solution_final

# Homework 3 solution_final - Homework#3 Solution ECE 15a 1(a...

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Unformatted text preview: Homework #3 Solution ECE 15a 1. (a) f = (a’b’c’+c)(a’b’c’+d’)+(cd’+b)(cd’+c)+ab’d’+ab’c’d = a’b’c’(d+d’)+cd’(a+a’)(b+b’)+bc(a+a’)(d+d’)+ab’d’(c+c’)+ab’c’d = a’b’c’d+a’b’c’d’+abcd’+a’bcd’+ab’cd’+a’b’cd’+abcd+a’bcd+abcd’+ab’c’d’ +ab’c’d (b) g = (x+yz)’+(y’z+yz’)(y’z+w’)+yz’w = x’(yz)’+y’z+yz’w’+yz’w = x’y’(w+w’)(z+z’)+y’z(w+w’)(x+x’)+yz’(w+w’)(x+x’) = wx’y’z+w’x’y’z+wx’y’z’+w’x’y’z’+wxy’z+w’xy’z+wxyz’+w’xyz’+wx’yz’ +w’x’yz’ (c) h = (x+z’)(x’+y)(x’+z’) = (xy+x’z’+yz’)(x’+z’) = xyz’+x’z’+yz’ = yz’(x+x’)+x’z’(y+y’) = xyz’+x’yz’+x’y’z’ 2. (a) f = (x’+y)’ = xy’(z+z’) = xy’z+xyz’ = Σ m(5,6) (b) g = xz+x’z’ = (xz+x’z’)(y+y’) = xyz+xy’z+x’yz’+x’y’z’ = Σ m(0,2,5,7) 3. (a) Truth table xyz f 000 1 001 0 010 0 011 1 100 1 101 0 110 0 111 0 (b) f = Π M(1,2,5,6,7) (c) f...
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Homework 3 solution_final - Homework#3 Solution ECE 15a 1(a...

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