# Boolean Algebra · Digital Circuits · GATE ECE

Start Practice## Marks 1

GATE ECE 2024

For the Boolean function $F(A, B, C, D) = \sum m(0,2,5,7,8,10,12,13,14,15)$, the essential prime implicants are _________.

GATE ECE 2022

Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

GATE ECE 2018

A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum
of products is given by
F = $$\overline A .\overline B .\ov...

GATE ECE 2014 Set 2

For an n - variable Boolean function maximum number of prime implicants is

GATE ECE 2014 Set 1

The Boolean expression
(X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

GATE ECE 2013

In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

GATE ECE 2007

The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is

GATE ECE 2006

The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where , "d" denotes don't care states...

GATE ECE 2005

The Boolean expression for the truth table shown is
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GATE ECE 2003

The number of distinct Boolean expressions of 4 variables is

GATE ECE 1999

The Logical expression $$Y = A + \overline A B$$ is equivalent to

GATE ECE 1998

The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is
...

GATE ECE 1998

Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the ...

GATE ECE 1990

The number of Boolean functions that can be generated by n variable is equal to:

## Marks 2

GATE ECE 2017 Set 1

Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F =...

GATE ECE 2016 Set 3

Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is
...

GATE ECE 2015 Set 2

A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$m(1,2,5,6,7) Which one of the ...

GATE ECE 2015 Set 1

The Boolean expression
F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$
converted into the canonical ...

GATE ECE 2014 Set 1

Consider the Boolean function,
F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\o...

GATE ECE 2009

If X=1 in the logic equation
$$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \o...

GATE ECE 2007

The Boolean expression
Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} \overline C \,D + AB\overline ...

GATE ECE 2006

The point p in the following figure is stuck- at-1. The output f will be
...

GATE ECE 2004

The Boolean expression AC + B$$\overline C $$ is equivalent to

GATE ECE 2004

A Boolean function 'f' of two variables x and y is defined as follows:
f(0,0)=f(0,1)=f(1,1)=1;f(1,0)=0
Assuming complements of x and y are not availab...

GATE ECE 2003

If the functions W, X, Y and Z are as follows
W= R+$$\overline P Q + \overline R $$ S
X = $$X = PQ\overline R \,\overline S + \overline P \,\overli...

GATE ECE 1999

For a binary half-subtractor having two inputs A and B, the correct set of Logical expressions for the output D(=Aminus B) and X(=Borrow) are

GATE ECE 1999

The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B\overline C + \overline A BC ...

## Marks 4

GATE ECE 1996

Given the Boolean function F in three variables R, S and T as
F=$$\,\overline R \,S\overline T + R\overline {S\,} T + RST$$
(a) Express F in the mi...

## Marks 5

GATE ECE 1999

In certain application, four inputs A, B, C, D (both true and complement forms available)are fed to logic circuit, producing an output F which operate...

GATE ECE 1996

Its is desired to generate the following three Boolean functions.
$$\eqalign{
& {F_1} = a\,\overline b \,c + \overline a \,b\overline c + bc ...

## Marks 10

GATE ECE 1995

A 'code converter' is to be designed to convert from the BCD(5421) to the normal BCD (8421). The input BCD combinations for each digit are below. A bl...

GATE ECE 1991

The four variable function f is given in terms of min-terms as:
f (A B C D ) = $$\sum {} $$m (2,3,8,10,11,12,14,15 .)
Using the K-map minimize the fu...