Boolean Algebra and Logic Minimization: GATE CS previous year questions (Digital Logic)

GATE CS 2026 Set 1MSQ1 markEasy (estimate)
GATE CS 2026 Set 1, Q.21
Consider the following Boolean expression of a function $F$ : $F (P, Q) = (P + Q) \oplus (P Q)$ Which of the following expressions is/are equivalent to $F$ ?
Boolean Algebra and Logic Minimization
GATE CS 2026 Set 1MSQ2 marksMedium (estimate)
GATE CS 2026 Set 1, Q.48
Consider a Boolean function $F$ with the following minterm expression: $F (P, Q, R, S) = \sum m (1, 2, 3, 4, 5, 7, 10, 12, 13, 14)$ Which of the following options is/are the min...
Boolean Algebra and Logic Minimization
GATE CS 2026 Set 2MCQ1 markEasy (estimate)
GATE CS 2026 Set 2, Q.16
Which one of the following options is not a property of Boolean Algebra? Note: $+$ is OR operation, $.$ is AND operation, and $^{'}$ is NOT operation
Boolean Algebra and Logic Minimization
GATE CS 2026 Set 2MCQ2 marksEasy (estimate)
GATE CS 2026 Set 2, Q.40
Consider the following 4-variable Boolean function $F (A, B, C, D) = Σ m (0, 1, 2, 3, 8, 9, 10, 11)$ Consider $A$ as MSB, $D$ as LSB. Which one of the following options rep...
Boolean Algebra and Logic Minimization
GATE CS 2025 Set 1MSQ1 markMedium (estimate)
GATE CS 2025 Set 1, Q.24
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...
Boolean Algebra and Logic Minimization
GATE CS 2025 Set 1MCQ2 marksEasy (estimate)
GATE CS 2025 Set 1, Q.42
Consider the following four variable Boolean function in sum-of-product form $F (b_{3}, b_{2}, b_{1}, b_{0}) = \sum (0, 2, 4, 8, 10, 11, 12) .$ where the value of the function is compute...
Boolean Algebra and Logic Minimization
GATE CS 2025 Set 2MSQ1 markEasy (estimate)
GATE CS 2025 Set 2, Q.31
Consider the following logic circuit diagram. Logic circuit with inputs Y and X feeding three branches into a 3-input OR gate with output F: top branch is a 2-input NAND gate of...
Boolean Algebra and Logic Minimization · Combinational Circuits
GATE CS 2025 Set 2MSQ2 marksEasy (estimate)
GATE CS 2025 Set 2, Q.43
Given the following Karnaugh Map for a Boolean function $F (w, x, y, z)$ : 4 by 4 Karnaugh Map for F(w, x, y, z) with row variables wx and column variables yz; rows 1 and 4 are 1,...
Boolean Algebra and Logic Minimization
GATE CS 2025 Set 2MSQ2 marksMedium (estimate)
GATE CS 2025 Set 2, Q.50
Which of the following Boolean algebraic equation(s) is/are CORRECT?
Boolean Algebra and Logic Minimization
GATE CS 2024 Set 1MSQ2 marksEasy (estimate)
GATE CS 2024 Set 1, Q.47
Consider a Boolean expression given by $F (X, Y, Z) = \sum (3, 5, 6, 7)$ . Which of the following statements is/are CORRECT?
Boolean Algebra and Logic Minimization
GATE CS 2024 Set 2MSQ1 markEasy (estimate)
GATE CS 2024 Set 2, Q.30
For a Boolean variable $x$ , which of the following statements is/are FALSE?
Boolean Algebra and Logic Minimization
GATE CS 2024 Set 2MSQ2 marksEasy (estimate)
GATE CS 2024 Set 2, Q.50
Consider 4-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below. $f 1 = \sum (0, 2, 3, 5, 7, 8, 11, 13)$ $f 2 = \sum (1, 3, 5, 7, 11, 13, 15)$ …
Combinational Circuits · Boolean Algebra and Logic Minimization
GATE CS 2021 Set 1MSQ2 marksMedium (estimate)
GATE CS 2021 Set 1, Q.52 (CS Q.42)
Consider the following Boolean expression. $F = (X + Y + Z) (X + Y) (Y + Z)$ Which of the following Boolean expressions is/are equivalent to $F$ ...
Boolean Algebra and Logic Minimization
GATE CS 2020MCQ2 marksEasy (estimate)
GATE CS 2020, Q.38 (CS Q.28)
Consider the Boolean function $z (a, b, c)$ represented by the logic circuit below. Logic circuit diagram with inputs a, b, c, an inverter on b, an AND gate combining not-b and c...
Boolean Algebra and Logic Minimization · Combinational Circuits
GATE CS 2019MCQ1 markEasy (estimate)
GATE CS 2019, Q.16 (CS Q.6)
Which one of the following is NOT a valid identity?
Boolean Algebra and Logic Minimization
GATE CS 2019NAT2 marksMedium (estimate)
GATE CS 2019, Q.60 (CS Q.50)
What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as $f = \sum (0, 2, 5, 7, 8, 10, 13, 15)$ ? Assume t...
Boolean Algebra and Logic Minimization
GATE CS 2018MCQ1 markEasy (estimate)
GATE CS 2018, Q.14 (CS Q.4)
Let $\oplus$ and $⊙$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?
Boolean Algebra and Logic Minimization
GATE CS 2018NAT2 marksMedium (estimate)
GATE CS 2018, Q.59 (CS Q.49)
Consider the minterm list form of a Boolean function $F$ given below. $F (P, Q, R, S) = \sum m (0, 2, 5, 7, 9, 11) + d (3, 8, 10, 12, 14)$ Here, $m$ denotes a minterm and $d$ den...
Boolean Algebra and Logic Minimization
GATE CS 2017 Set 1NAT1 markMedium (estimate)
GATE CS 2017 Set 1, Q.21 (CS Q.21)
Consider the Karnaugh map given below, where X represents "don't care" and blank represents 0. 4 by 4 Karnaugh map for a 4-variable Boolean logic function with row variables dc...
Boolean Algebra and Logic Minimization · Combinational Circuits
GATE CS 2017 Set 2MCQ2 marksMedium (estimate)
GATE CS 2017 Set 2, Q.27 (CS Q.27)
If $w, x, y, z$ are Boolean variables, then which one of the following is INCORRECT?
Boolean Algebra and Logic Minimization
GATE CS 2017 Set 2MCQ2 marksMedium (estimate)
GATE CS 2017 Set 2, Q.28 (CS Q.28)
Given $f (w, x, y, z) = \sum m (0, 1, 2, 3, 7, 8, 10) + \sum d (5, 6, 11, 15)$ , where $d$ represents the don’t-care condition in Karnaugh maps. Which of the following is a minimum product-of-s...
Boolean Algebra and Logic Minimization
GATE CS 2016 Set 1MCQ1 markEasy (estimate)
GATE CS 2016 Set 1, Q.16 (CS Q.6)
Consider the Boolean operator $#$ with the following properties: $x #0 = x$ , $x #1 = x ˉ$ , $x # x = 0$ and $x # x ˉ = 1$ . Then $x # y$ is equivalent to
Boolean Algebra and Logic Minimization
GATE CS 2016 Set 2MCQ1 markEasy (estimate)
GATE CS 2016 Set 2, Q.18 (CS Q.8)
Let $x_{1} \oplus x_{2} \oplus x_{3} \oplus x_{4} = 0$ where $x_{1}, x_{2}, x_{3}, x_{4}$ are Boolean variables, and $\oplus$ is the XOR operator. Which one of the following must always be TRUE?
Boolean Algebra and Logic Minimization
GATE CS 2015 Set 1MCQ2 marksEasy (estimate)
GATE CS 2015 Set 1, Q.38 (CS Q.28)
The binary operator $\neq =$ is defined by the following truth table: | $p$ | $q$ | $p \neq = q$ | | :---: | :---: | :---: | | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | Wh...
Boolean Algebra and Logic Minimization
GATE CS 2015 Set 1MCQ2 marksMedium (estimate)
GATE CS 2015 Set 1, Q.49 (CS Q.39)
Consider the operations: $f (X, Y, Z) = X^{'} Y Z + X Y^{'} + Y^{'} Z^{'} and g (X, Y, Z) = X^{'} Y Z + X^{'} Y Z^{'} + X Y .$ Which one of the following is correct?
Boolean Algebra and Logic Minimization
GATE CS 2015 Set 2NAT2 marksMedium (estimate)
GATE CS 2015 Set 2, Q.47 (CS Q.37)
The number of min-terms after minimizing the following Boolean expression is _____. $[D^{'} + A B^{'} + A^{'} C + A C^{'} D + A^{'} C^{'} D]^{'}$
Boolean Algebra and Logic Minimization
GATE CS 2015 Set 3MCQ1 markEasy (estimate)
GATE CS 2015 Set 3, Q.12 (CS Q.2)
Let $#$ be a binary operator defined as $X # Y = X^{'} + Y^{'}$ where $X$ and $Y$ are Boolean variables. Consider the following two statements. (S1)…
Boolean Algebra and Logic Minimization
GATE CS 2015 Set 3NAT2 marksMedium (estimate)
GATE CS 2015 Set 3, Q.53 (CS Q.43)
The total number of prime implicants of the function $f (w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is _____.
Boolean Algebra and Logic Minimization
GATE CS 2015 Set 3MCQ2 marksEasy (estimate)
GATE CS 2015 Set 3, Q.54 (CS Q.44)
Given the function $F = P^{'} + QR$ , where $F$ is a function in three Boolean variables $P, Q$ and $R$ and $P^{'} = \neg P$ , consider the following statements. (S1)…
Boolean Algebra and Logic Minimization
GATE CS 2014 Set 1MCQ1 markEasy (estimate)
GATE CS 2014 Set 1, Q.17 (CS Q.7)
Consider the following Boolean expression for $F$ : $F (P, Q, R, S) = P Q + P ˉ QR + P ˉ Q R ˉ S$ The minimal sum-of-products form of $F$ is
Boolean Algebra and Logic Minimization
GATE CS 2014 Set 2MCQ1 markEasy (estimate)
GATE CS 2014 Set 2, Q.16 (CS Q.6)
The dual of a Boolean function $F (x_{1}, x_{2}, \dots, x_{n}, +, \cdot,^{'})$ , written as $F^{D}$ , is the same expression as that of $F$ with $+$ and $\cdot$ swapped. $F$ is said to be se...
Boolean Algebra and Logic Minimization
GATE CS 2014 Set 3MCQ1 markEasy (estimate)
GATE CS 2014 Set 3, Q.17 (CS Q.7)
Consider the following minterm expression for $F$ : $F (P, Q, R, S) = \sum m (0, 2, 5, 7, 8, 10, 13, 15)$ The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-...
Boolean Algebra and Logic Minimization
GATE CS 2014 Set 3MCQ2 marksEasy (estimate)
GATE CS 2014 Set 3, Q.65 (CS Q.55)
Let $\oplus$ denote the Exclusive OR (XOR) operation. Let '1' and '0' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and…
Boolean Algebra and Logic Minimization
GATE CS 2013MCQ1 markEasy (estimate)
GATE CS 2013, Q.21 (CS Q.21)
Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$ ?
Boolean Algebra and Logic Minimization
GATE CS 2012MCQ1 markEasy (estimate)
GATE CS 2012, Q.6 (CS Q.6)
The truth table $X 0011 Y 0101 f (X, Y) 0011$ represents the Boolean function
Boolean Algebra and Logic Minimization
GATE CS 2012MCQ2 marksMedium (estimate)
GATE CS 2012, Q.30 (CS Q.30)
What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don't care term. Four-variable Karnaugh map for variables a, b, c, d with specified 1s and do...
Boolean Algebra and Logic Minimization · Boolean Algebra and Logic Minimization
GATE CS 2011MCQ1 markEasy (estimate)
GATE CS 2011, Q.14 (CS Q.14)
The simplified SOP (Sum of Product) form of the Boolean expression $(P + Q + R) \cdot (P + Q + R) \cdot (P + Q + R)$ is
Boolean Algebra and Logic Minimization

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