1.  Which one of the following expressions does NOT represent exclusive NOR of x and y? 
a.  xy + x' y' 
b.  x ^ y' where ^ is XOR 
c.  x' ^ y where ^ is XOR 
d.  x' ^ y' where ^ is XOR 
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Answer: (d).x' ^ y' where ^ is XOR

2.  The simplified SOP (Sum Of Product) form of the boolean expression (P + Q' + R') . (P + Q' + R) . (P + Q + R') is 
a.  (P'.Q + R') 
b.  (P + Q'.R') 
c.  (P'.Q + R) 
d.  (P.Q + R) 
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Answer: (b).(P + Q'.R')

3.  The minterm expansion of f(P, Q, R) = PQ + QR' + PR' is 
a.  m2 + m4 + m6 + m7 
b.  m0 + m1 + m3 + m5 
c.  m0 + m1 + m6 + m7 
d.  m2 + m3 + m4 + m5 
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Answer: (a).m2 + m4 + m6 + m7

4.  What is the minimum number of gates required to implement the Boolean function (AB+C)if we have to use only 2input NOR gates? 
a.  2 
b.  3 
c.  4 
d.  5 
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Answer: (b).3

5.  If P, Q, R are Boolean variables, then (P + Q')(PQ' + PR)(P'R' + Q') simplifies 
a.  PQ' 
b.  PR' 
c.  PQ' + R 
d.  PR'' + Q 
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Answer: (a).PQ'

6.  How many 3to8 line decoders with an enable input are needed to construct a 6to64 line decoder without using any other logic gates? 
a.  7 
b.  8 
c.  9 
d.  10 
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Answer: (c).9

7.  Consider the following Boolean function of four variables: f(w,x,y,z) = ∑(1,3,4,6,9,11,12,14) The function is: 
a.  independent of one variables 
b.  independent of two variables 
c.  independent of three variables 
d.  dependent on all the variables 
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Answer: (b).independent of two variables

8.  Let f(w, x, y, z) = ∑(0, 4, 5, 7, 8, 9, 13, 15). Which of the following expressions are NOT equivalent to f? 
a.  x'y'z' + w'xy' + wy'z + xz 
b.  w'y'z' + wx'y' + xz 
c.  w'y'z' + wx'y' + xyz + xy'z 
d.  x'y'z' + wx'y' + w'y 
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Answer: (d).x'y'z' + wx'y' + w'y

9.  Define the connective * for the Boolean variables X and Y as: X * Y = XY + X' Y'. Let Z = X * Y.
Consider the following expressions P, Q and R. P: X = Y⋆Z Q: Y = X⋆Z R: X⋆Y⋆Z=1 Which of the following is TRUE? 
a.  Only P and Q are valid 
b.  Only Q and R are valid 
c.  Only P and R are valid 
d.  All P, Q, R are valid 
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Answer: (d).All P, Q, R are valid

10.  Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of n variables. What is the minimum size of the multiplexer needed? 
a.  2^n line to 1 line 
b.  2^(n+1) line to 1 line 
c.  2^(n1) line to 1 line 
d.  2^(n2) line to 1 line 
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Answer: (c).2^(n1) line to 1 line
