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homework_3_ece15a_11

homework_3_ece15a_11 - Homework#3 due January 31 at noon...

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Homework #3 January 18, 2011 1 Homework #3 due January 31 at noon ECE 15a Winter 2011 1. Express each of the following functions in disjunctive normal form (DNF) in the smallest possi- ble number of variables: (2p) (a) f=(a’b’c’+c)(a’b’c’+d’)+(cd’+b)(cd’+c)+ab’d’+ab’c’d (2p) (b) g=(x+yz)’+(y’z+yz’)(y’z+w’)+yz’w (2p) (c) h=(x+z’)(x’+y)(x’+z’) 2. Write each of the following functions in DNF in three variables x,y,z. Express your results using the m-notation. (5p) (a) f= (x’+y)’ (5p) (b) g=xz+x’z’ 3. The function f(x,y,z) is 1 if either x = 0 and y=z=1, or if z=0 and y=0; and is 0 otherwise. (a) (2p) Construct truth table for f(x,y,z). (b) (2p) Express f using the M-notation. (c) (2p) Express f using the m-notation. 4. Express each of the following functions in conjunctive normal form (CNF) in the smallest pos- sible number of variables:
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