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

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Question 1

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)? [GATE||2021 ||SET1||MSQ || 1-mark]

  • XY’ +Z’

  • (X + Z’)(Y’ + Z’)


  • (X’+Y’+ Z’)(X +Y’)(Y +Z’)


  • XY’+YZ’ + X’Y’Z’ 


Question 2

Consider a Boolean expression given by F(X,Y,Z) = Σ(3,5,6,7) Which of the following statements is/are CORRECT? [GATE|| 2024 SET1||MSQ || 2-mark ]

  • F (X,Y,Z)= Π (0,1,2,4)

  • F (X,Y,Z)= XY+YZ+XZ

  • F (X,Y,Z) is independent of input Y

  • F (X,Y,Z) is independent of input X

Question 3

Given the following Karnaugh Map for a Boolean function F(w,x,y,z) :

q33
k'map


Which one or more of the following Boolean expression(s) represent(s) F ? [GATE || 2025 ||SET 2|| MSQ || 2-mark ]

  • W'X'Y'Z' + WX'Y'Z' + W'X'YZ' + WX'YZ' + XZ

  • W'X'Y'Z' + W'X'YZ' + WX'YZ + XZ

  • W'X'Y'Z' + WX'Y'Z' + WX'YZ + XZ

  • X'Z' +XZ

Question 4

Which of the following Boolean algebraic equation(s) is/are CORRECT? [GATE || 2025 ||SET 2|| MSQ || 2-mark ]

  • A'BC + AB'C' + A'B'C' + AB'C + ABC = BC + B'C' + A'B'

  • AB + A'C +BC = AB + A'C

  • (A +C)(A' +B) = AB + A'C

  • {(A + B' + D')(C +D)(A' +C +D)(A +B +D')}' = A'D + C'D'

Question 5

Let X  be a 3-variable Boolean function that produces output as '1' when at least two of the input variables are '1'. Which of the following statement(s) is/are CORRECT, where a,b,c,d,e  are Boolean variables ? [GATE|| 2025 ||SET 2||MSQ || 2-mark ]

  • X(a,b, X(c,d,e))=X(X(a,b,c),d,e)

  • X(a,b,X(a,b,c))=X(a,b,c)

  • X(a,b,X(a,c,d))=(X(a,b,a)  AND  X(c,d,c))

  • X(a,b,c)= X(a, X(a,b,c),X(a,c,c))

Question 6

Consider the following four-variable Boolean function in sum-of-product form F(b3,b2,b1,b0) = ∑(0,2,4,8,10,11,12) Where the value of the function is computed by considering b3b2b1b0 ​ as a 4-bit binary number, where b3 3​ denotes the most significant bit and b0  denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for F ? [GATE || 2025 || SET 1|| MCQ || 1-mark]

  • b1'b0' + b2'b0' + b1b2'b3

  • b1'b0' + b2'b0'

  • b2'b0' + b1b2b3

  • bo'b2' + b3'

Question 7

The total number of prime implicants of the function f(w,x,y,z) = Σ(0, 2, 4, 5, 6, 10) is ______. [GATE||2015||SET3||NAT||1MARKS]

  • 3

Question 8

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


unnamed-17


Which one of the following minterm lists represents the circuit given above? [GATE 2020||MCQ|| 2 marks]


  • Z = Σ(0,1,3,7)

  • Z = Σ(2,4,5,6,7)

  • Z = Σ(1,4,5,6,7)

  • Z = Σ(2,3,5)

Question 9

What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below? [GATE|| 2010|| MCQ||2 Mark]

unnamed-11


  • (Q+R)'

  • (P+Q)'

  • (P+R)'

  • (P+Q+R)'

Question 10

Consider the following minterm expression for F :

F(P, Q, R, S) = ∑0, 2, 5, 7, 8, 10, 13, 15

The minterms 2, 7, 8 and 13 are ‘do not care’ terms. The minimal sum-of-products from for F is ? [GATE||2014||SET3||MCQ||1 MARKS]


  • QS' + Q'S

  • Q'S' + QS

  • Q'R'S' + Q'RS' + QR'S + QRS

  • P'Q'S' + P'QS + PQS + PQ'S'

There are 21 questions to complete.

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