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    • Logic functions and Minimization

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    Question 1

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

    • A

      xy+x'y'

    • B

      x⊕y'

    • C

      x'⊕y

    • D

      x'⊕y'

    Question 2

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

    GATECS201113
    • A

      A

    • B

      B

    • C

      C

    • D

      D

    Question 3

    What is the minimized sum-of-products (SOP) switching expression corresponding to the Boolean function

    f(A, B, C, D) = Σ(1, 4, 5, 9, 11, 12)?

    (GATE 2005 | MCQ | 2-mark)

    • A

      BC'D + A'CD + AB'D

    • B

      BC'D' + A'C'D + AB'D

    • C

      ABC' + ACD + B'C'D

    • D

      ACD' + A'BC' + AC'D'

    Question 4

    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

    Question 5

    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

    Question 6

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

     
    • A

      b'd'

    • B

      b'd' + b'c'

    • C

      b'd' + a'b'c'd'

    • D

      b'd' + b'c' + c'd'

    Question 7

    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?


    k-Map2
    K-Map

     

    • A

      b'd'+a'd'

    • B

      a'b'+b'd'+a'b'd'

    • C

      b'd'+a'b'd'

    • D

      a'b'+b'd'+a'd'

    Question 8

    Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit

    14

    15


    • A

      [Tex]\sum m(4,6)[/Tex]

    • B

      [Tex]\sum m(4,8)[/Tex]

    • C

      [Tex]\sum m(6,8)[/Tex]

    • D

      [Tex]\sum m(4,6,8)[/Tex]

    Question 9

    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

    Question 10

    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.

    There are 104 questions to complete.

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