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# HW3 - (3p(a f =(u v w(uv u’w)’(3p(b g = xy xz...

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Homework #3 January 22, 2008 1 Homework #3 due February 4 at noon ECE 15a Winter 2008 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)(uv’+u’w)’ (3p) (b) g=xyz’+(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= 0 and z=1, 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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