HW3_Sol

HW3_Sol - ECE 15a Winter 2008 Homework #3 Solutions 1. a. f...

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ECE 15a Winter 2008 Homework #3 Solutions 1. a. f = (u + v’ + w) (uv’ + u’w)’ = (u + v’ + w) [(u’ + v) (u + w’)] = (u + v’ + w) [uv + u’w’] = uv + u’v’w’ + uvw = uv(w + w’) + u’v’w’ + uvw = uvw + uvw’ + uvw + u’v’w’ = uvw + uvw’ + u’v’w’ b. g = xyz’ + [(x+y)(x+z’)] = xyz’ + [ x + yz’] = xyz’ + x(y+y’)(z+z’) + yz’(x+x’) = xyz’ + xyz + xyz’ + xy’z + xy’z’ + xyz’ + x’yz’ = xyz’ + xyz + xy’z + xy’z’ + x’yz’ c. h = [(x+y)(x+y’)] (x’+z’) = [xz + x’y] (x’+z’) = xz + xy’z = x(y+y’)z + xy’z = xyz + xy’z
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2. a. f = x + y’ = x (y+y’) (z+z’) + y’ (x+x’) (z+z’) = x [yz + yz’ + y’z + y’z’] + y’ [ …. . ] = xyz + xyz’ + xy’z + xy’z’ + xy’z + xy’z’ + x’y’z + x’y’z’ = xyz + xyz’ + xy’z + xy’z’ + x’y’z + x’y’z’ b. g = xz’ + x’z = x (y+y’) z’ + x’ (y+y’) z = xyz’ + xy’z’ + x’yz + x’y’z 3. x
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This note was uploaded on 01/13/2010 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.

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HW3_Sol - ECE 15a Winter 2008 Homework #3 Solutions 1. a. f...

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