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# hmwk3 - (3p(a f =(u v’ w(uv’ u’w)’(3p(b g = xy’...

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Homework #3 January 23, 2007 1 Homework #3 due February 6 at noon ECE 15a Winter 2007 1. Express each of the following functions in disjunctive normal form (DNF) in the small- est possible number of variables: (3p) (a) f=(u’+v+w)(u’v+uw)’ (3p) (b) g=x’yz+(x’+y)(x’+z) (3p) (c) h=(x’+y)(x’+y’)(x+z) 2. Write each of the following functions in DNF in the three variables x,y,z: (5p) (a) f= x’+y’ (5p) (b) g=xz+x’z’ (3p) 3. Write the function of 3 variables x,y,z which is 1 if either x = y= 1 and z=0, or if x=z=1 and y=0; and is 0 otherwise. 4. Express each of the following functions in conjunctive normal form ( CNF) in the smallest possible number of variables:
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Unformatted text preview: (3p) (a) f = (u+v’+w)(uv’+u’w)’ (3p) (b) g = xy’+xz’+xy (3p) (c) h= (x’y’+xy’z’+xyz+x’yz’t+t’)’ 5. Write each of the following functions in CNF in the 3 variables x,y,z: (3p) (a) (x+y)(x’+y’) (3p) (b) xz+x’z’ (3p) 6. Change the following function from DNF to CNF: f=uv+u’v+u’v’ (5p) 7. Change the following function from CNF to DNF f= (u+v+w’)(u+v+w)(u+v’+w’)(u’+v+w)(u’+v’+w’)(u’+v’+w) 8. Do the following problems from CHR: (5p) (a) 3.10 (a) (5p) (b) 3.14 (b) (5p) (c) 3.15 (d) (5p) (d) 3.16 (5p) (e) 3.25 (a) (10p) (f) 3.26 (a)...
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