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    • GATE || DIGITAL LOGIC || LOGIC GATE || PYQ (2010 TO 2025)

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    Question 1

    Which one of the following circuits isΒ NOTΒ equivalent to a 2-input XNOR (exclusive NOR) gate? [GATE||2011||MCQ||1MARKS]

    • A
      qwe1
      .
    • B
      qwe2
      .
    • C
      qwe3
      .
    • D
      qwe4
      .

    Question 2

    The truth tableΒ Β represents the Boolean function [GATE||2012||MCQ||1MARKS]

    X

    Y

    (X,Y)

    0

    0

    0

    0

    1

    0

    1

    0

    1

    1

    1

    1

    • A

      X

    • B

      X + Y

    • C

      X βŠ• Y

    • D

      Y

    Question 3

    Which one of the following expressions does NOT represent exclusive NOR of x and y? [GATE 2013 || MCQ || 1 MARKS ]


    • A

      xy+x'y'

    • B

      xβŠ•y'


    • C

      x'βŠ•y

    • D

      x'βŠ•y'


    Question 4

    Let βŠ• denote the Exclusive OR (XOR) operation. Let β€˜1’ and β€˜0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q:

    F(P, Q) = ((1βŠ•P)βŠ•(PβŠ•Q)) βŠ• ((PβŠ•Q) βŠ• (QβŠ•O))

    The equivalent expression for F is [GATE||2014||SET3||MCQ||2MARKS]


    • A

      P+Q

    • B

      (P+Q)'

    • C

      P⨁Q

    • D

      (P⨁Q)'

    Question 5

    Let, x1βŠ•x2βŠ•x3βŠ•x4 = 0 where x1, x2, x3, x4 are Boolean variables, and βŠ• is the XOR operator. Which one of the following must always be TRUE? [GATE||2016||SET2||1MARKS]


    • A

      x1x2 x3x4 = 0

    • B

      x1x3+x2 = 0

    • C

      x1 'βŠ•x3 '= x2 'βŠ• x4 '

    • D

      x1 + x2 + x3 + x4 = 0


    Question 6

    Consider the Boolean operator # with the following properties: x#0 = x, x#1 = x', x#x = 0 and x#x' = 1 Then x#y is equivalent to [GATE||2016||SET1||1MARKS]

    • A

      x'y + xy'

    • B

      xy' + (xy)

    • C

      x'y + xy

    • D

      xy + (xy)'

    Question 7

    Which one of the following is NOT a valid identity?[GATE|| 2019 || MCQ || 1 Mark]

    • A

      (x + y) βŠ• z = x βŠ• (y + z)

    • B

      (x βŠ• y) βŠ• z = x βŠ• (y βŠ• z)


    • C

      x βŠ• y = x + y, if xy = 0

    • D

      x βŠ• y = (xy + x'y')'


    Question 8

    Consider the following logic circuit diagram.

    cvjhg
    Circuit


    Which is/are the CORRECT option(s) for the output functionΒ F ? [GATE || 2025 || SET 2|| MSQ || 2-mark]

    • (XY)'

    • X' + Y' + XY'

    • (XY)' + X' + XY'

    • X + Y'

    Question 9

    Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays.

    hgvhbjk
    circuit


    Which of the following statements about the circuit is/are CORRECT? [GATE|| 2024 ||SET 1||MSQ || 2-mark ]

    • With no propagation delays, the output Y is always logic Zero

    • With no propagation delays, the output Y is always logic One

    • With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One

    • With propagation delays, the output Y can have a transient logic Zero after X transitions from logic One to logic Zero

    Question 10

    Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form as given below.Β 

    f1 = βˆ‘(0,2,3,5,7,8,11,13)Β 

    f2 = βˆ‘(1,3,5,7,11,13, 15)Β 

    f3 = βˆ‘(0,1,4,11)Β 

    f4 = βˆ‘(0,2,6,13)

    fcghjhg
    circuit


    With respect to the circuit given above, which of the following options is/are CORRECT? [GATE|| 2024 SET2|| MSQ ||1-mark]

    • Y= βˆ‘(0,1,2,11,13)

    • Y= Ξ  (3,4,5,6,7,8,9,10,12,14,15)

    • Y= βˆ‘(0,1,2,3,4,5,6,7)

    • Y= Ξ  (8,9,10,11,12,13,14,15)

    There are 11 questions to complete.

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