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
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)
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
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 2-input NOR gates?
a. 2
b. 3
c. 4
d. 5
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
Answer: (a).PQ'

6. How many 3-to-8 line decoders with an enable input are needed to construct a 6-to-64 line decoder without using any other logic gates?
a. 7
b. 8
c. 9
d. 10
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
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
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
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^(n-1) line to 1 line
d. 2^(n-2) line to 1 line
Answer: (c).2^(n-1) line to 1 line

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