Logic functions and Minimization

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Question 1

Consider the Boolean function z(a,b,c).

Which one of the following minterm lists represents the circuit given above ?

  • z = ∑(0, 1, 3, 7)

  • z = ∑(1, 4, 5, 6, 7)

  • z = ∑(2, 4, 5, 6, 7)

  • z = ∑(2, 3, 5)

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Question 2

Let p and q be two propositions. Consider the following two formulae in propositional logic. 

S1:  (¬p∧(p∨q))→q
S2:  q→(¬p∧(p∨q))

Which one of the following choices is correct?

  • Both S1 and S2 are tautologies.

  • S1 is a tautology but S2 is not a tautology

  • S1 is not a tautology but S2 is a tautology

  • Neither S1 nor S2 is a tautology

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Question 3

Consider the following Boolean expression. 

F=(X+Y+Z)(X'+Y)(Y'+Z)

Which of the following Boolean expressions is/are equivalent to F' (complement of F)?

  • (X'+Y'+Z')(X+Y')(Y+Z')

  • XY'+Z'

  • (X+Z')(Y'+Z')

  • XY'+YZ'+X'Y'Z'

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Question 4

Which one of the following expressions does NOT represent exclusive NOR of x and y?

  • xy+x'y'

  • x⊕y'

  • x'⊕y

  • x'⊕y'

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Question 5

What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term.

 

  • b'd'

  • b'd' + b'c'

  • b'd' + a'b'c'd'

  • b'd' + b'c' + c'd'

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Question 6

Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate?

GATECS201113

  • A

  • B

  • C

  • D

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Question 7

The simplified SOP (Sum Of Product) form of the boolean expression (P + Q' + R') . (P + Q' + R) . (P + Q + R') is

  • (P'.Q + R')

  • (P + Q'.R')

  • (P'.Q + R)

  • (P.Q + R)

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Question 8

The minterm expansion of f(P, Q, R) = PQ + QR' + PR' is

  • m2 + m4 + m6 + m7

  • m0 + m1 + m3 + m5

  • m0 + m1 + m6 + m7

  • m2 + m3 + m4 + m5

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Question 9

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?

  • 2

  • 3

  • 4

  • 5

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Question 10

In the Karnaugh map shown below, X denotes a don't care term. What is the minimal form of the function represented by the Karnaugh map?


A)   


B) 

C) 

D) 

  • A

  • B

  • C

  • D

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