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GATE CSE

Boolean Algebra

Digital Logic

Previous Years Questions

Marks 1

More
Which one of the following is NOT a valid identity?
GATE CSE 2019
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,...
GATE CSE 2016 Set 2
Consider the Boolean operator $$ \ne $$ with the following properties: $$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \...
GATE CSE 2016 Set 1
Let $$ \ne $$ be a binary operator defined as $$X \ne Y = X' + Y'$$ where $$š‘‹$$ and $$š‘Œ$$ are Boolean variables. Consi...
GATE CSE 2015 Set 3
Consider the following combinational function block involving four Boolean variables $$x, y, a,$$ $$b$$ where $$x, a, b...
GATE CSE 2014 Set 3
Consider the following Boolean expression for $$F:$$ $$F\left( {P,\,Q,\,R,\,S} \right) = PQ + \overline P QR + \overlin...
GATE CSE 2014 Set 1
The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, i...
GATE CSE 2014 Set 2
Which one of the following expressions does NOT represent exclusive NOR of $$x$$ and $$y?$$
GATE CSE 2013
The simplified $$SOP$$ (Sum of product) form of the Boolean expression $$\left( {P + \overline Q + \overline R } \righ...
GATE CSE 2011
Which one of the following circuits is NOT equivalent to a $$2$$-input $$XNOR$$ (exclusive NOR) gate
GATE CSE 2011
The minters expansion of $$f\left( {P,Q,R} \right) = PQ + Q\overline R + P\overline R $$ is
GATE CSE 2010
What is the minimum number of gates required to implement the Boolean function $$(AB+C)$$ if we have to use only $$2$$-i...
GATE CSE 2009
Given $${f_1},$$ $${f_3},$$ and $$f$$ in canonical sum of products form (in decimal) for the circuit. $$${f_1} = \sum {m...
GATE CSE 2008
Consider the following Boolean function with four variables $$F\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {1,\,3,\,4...
GATE CSE 2007
The Boolean function $$x'y' +xy +x'y$$ is equivalent to
GATE CSE 2004
Let $$^ * $$ be defined as $${x^ * }y = \overline x + y,$$ Let $$z = {x^ * }y.$$ Value of $${z^ * }x$$ is
GATE CSE 1997

Marks 2

More
Consider the following Boolean expression. $$F = (X + Y + Z)(\overline X + Y)(\overline Y + Z)$$ Which of the followin...
GATE CSE 2021 Set 1
Consider the Boolean function z(a,b,c). Which one of the following minterm lists represents the circuit given above?...
GATE CSE 2020
Consider three 4-variable functions f1, f2 and f3, which are expressed in sum-of-minterms as f1 = Ī£(0, 2, 5, 8, 14), f...
GATE CSE 2019
Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the fo...
GATE CSE 2018
Consider a carry lookahead adder for adding two $$n$$-bit integers, built using gates of fan-in at most two. The time to...
GATE CSE 2016 Set 1
The total number of prime implicants of the function $$f\left( {w,x,y,z} \right) = \sum {\left( {0,2,4,5,6,10} \right)}...
GATE CSE 2015 Set 3
Given the function $$F = Pā€² + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$...
GATE CSE 2015 Set 3
A half adder is implemented with $$XOR$$ and $$AND$$ gates. A full adder is implemented with two half adders and one $$O...
GATE CSE 2015 Set 2
The number of min-terms after minimizing the following Boolean expression is _______________ . $$$\left[ {D' + AB' + A'...
GATE CSE 2015 Set 2
Consider the operations $$f\left( {x,y,z} \right) = X'YZ + XY' + Y'Z'$$ and $$g\left( {x,y,z} \right) = X'YZ + X'YZ' + ...
GATE CSE 2015 Set 1
The binary operator $$ \ne $$ is defined by the following truth table. .tg {border-collapse:collapse;border-spacing:0;...
GATE CSE 2015 Set 1
Let $$ \oplus $$ denote the exclusive $$OR\left( {XOR} \right)$$ operation. Let $$'1'$$ and $$'0'$$ denote the binary co...
GATE CSE 2014 Set 3
What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below? ...
GATE CSE 2010
If $$P, Q, R$$ are Boolean variables, then $$\left( {P + \overline Q } \right)$$ $$\left( {P.\overline Q + P.R} \right)...
GATE CSE 2008
Let $$f\left( {w,x,y,z} \right) = \sum {\left( {0,4,5,7,8,9,13,15} \right).} $$ Which of the following expressions are N...
GATE CSE 2007
Consider a Boolean function $$f(w, x, y, z).$$ Suppose that exactly one of its inputs is allowed to change at a time. If...
GATE CSE 2006
Which are the essential prime implicants of the following Boolean function? $$F\left( {a,b,c} \right) = {a^1}c + a{c^1} ...
GATE CSE 2004
$$f\left( {A,B} \right) = A' + B$$ Simplified expression for function $$f((x+y,y),z)$$ is
GATE CSE 2002
Transform the following logic circuit (without expressing its switching function) into an equivalent logic circuit that ...
GATE CSE 2002
Consider the following logic circuit whose inputs are functions $${f_1},$$ $${f_2},$$ $${f_3},$$ and output is $$f.$$ ...
GATE CSE 2002
The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$$x+y+z=1$$$ $$$xy=0$$$ $$$xz+w=1$$$ $$$xy ...
GATE CSE 2000
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?
GATE CSE 1999
Consider the logic circuit shown in Figure below. The functions $${f_1},$$ $${f_2}$$ and $$f$$ (in canonical sum of prod...
GATE CSE 1997
Let $$f\left( {x,y,z} \right) = \overline x + \overline y x + xz$$ be a switching function. Which one of the following ...
GATE CSE 1997
Two $$NAND$$ gates having open collector outputs are tied together as shown in fig. The logic function $$Y,$$ implemente...
GATE CSE 1990

Marks 5

More
A circuit outputs a digit in the form of $$4$$ bits. $$0$$ is represented by $$0000$$, $$1$$ by $$0001..., $$ $$9$$ by $...
GATE CSE 2004
Consider the following circuit composed of $$XOR$$ gates are non-inverting buffers. The non-inverting buffers have del...
GATE CSE 2003
Express the function $$f( x, y, z)= xy'+ yz'$$ with only one complement operation and one or more $$AND/OR$$ operations....
GATE CSE 2002
A logic network has two data inputs $$A$$ and $$B,$$ and two control inputs $${C_0}$$ and $${C_1}$$. It implements the f...
GATE CSE 1996
Find the minimum sum of products form of the logic function $$f\left( {A,B,C,D} \right) = \sum d \left( {3,11,12,14} \r...
GATE CSE 1991
Find the minimum product of sums of the following expression $$f = ABC + \overline A \,\overline B \,\overline C .$$ ...
GATE CSE 1990
Show with the help of a block diagram represent Boolean function: $$f=AB+BC+CA$$ can be realized using only $$4:1$$ mul...
GATE CSE 1990

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