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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 y z f 0 0 1 1 1 0 1 1 For all other combinations f = 0 0 0 0 Therefore the function, f = x’y’z + xy’z 4. a. f = (u+v+w) (uv + u’w)’ = (u+v+w) [ (u’ + v’) (u + w’) ] = (u+v+w) [(u’ + v’+ww’) (u + w’+vv’)] = (u+v+w)( u’ + v’+w) (u’ + v’+w’) (u + w’+v) (u + w’+v’) ------------ CNF form
b. g = xy + xz + xy’

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

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