homework_3_ece15a_11

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

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Unformatted text preview: 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 possible 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 possible number of variables: (3p) (a) f = (u+w)’(uv+u’w)’ (3p) (b) g = x’y’z+xy’z’+xy (3p) (c) h= (x’y’+xy’z’+x’z’t+t’)’ 5. Given the minterm expansion of f(a,b,c,d) = Σm(0, 2, 3,7,10,11) (2 p) (a) Write the minterm expansion of f’(a,b,c,d) (2 p) (b) Write the maxterm expansion of f(a,b,c,d) (2 p) (c) Write the maxterm expansion of f’(a,b,c,d) (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’) 8. (5p) Reduce to a minimum sum of products (3 terms): ( c ⊕ d ) ( a + b ) + ab 9.(5p) Simplify the following expression. Try to find an expression with the fewest number of literals. xz ( x + y + z + w ) ( x + z + w + v ) ( x + z + w + v ) 10. (5p) Determine, if XOR is distributive over addition. Homework #3 January 18, 2011 1 ...
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This note was uploaded on 02/26/2011 for the course ECE 15A taught by Professor M during the Winter '08 term at UCSB.

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