Boolean Algebra · Digital Circuits · GATE ECE

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Marks 1

1

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 2024
2

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

GATE ECE 2022
3
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 = $$\overline A .\overline B .\overline C + \overline A .B.\overline C + A.\overline B .\overline C $$

where, $$\overline A $$, $$\overline B $$, and $$\overline C $$ are the complements of the respective variables. The product of sums (POS) form of the function F is
GATE ECE 2018
4
For an n - variable Boolean function maximum number of prime implicants is
GATE ECE 2014 Set 2
5
The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to
GATE ECE 2014 Set 1
6
In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are
GATE ECE 2013
7
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 2007
8
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 2006 Digital Circuits - Boolean Algebra Question 26 English
GATE ECE 2006
9
The Boolean expression for the truth table shown is
A B C D
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 0
GATE ECE 2005
10
The number of distinct Boolean expressions of 4 variables is
GATE ECE 2003
11
The Logical expression $$Y = A + \overline A B$$ is equivalent to
GATE ECE 1999
12
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 Boolean function.
GATE ECE 1998
13
The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is GATE ECE 1998 Digital Circuits - Boolean Algebra Question 30 English
GATE ECE 1998
14
The number of Boolean functions that can be generated by n variable is equal to:
GATE ECE 1990

Marks 2

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 $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
GATE ECE 2017 Set 1
2
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 2016 Set 3 Digital Circuits - Boolean Algebra Question 10 English
GATE ECE 2016 Set 3
3
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 product of sums given below is equal to the funtion F(X, Y, Z)?
GATE ECE 2015 Set 2
4
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 product of sum (POS)from is
GATE ECE 2015 Set 1
5
Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\overline z $$ Which one of the following is the complete set of essential prime implicants?
GATE ECE 2014 Set 1
6
If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$$ then
GATE ECE 2009
7
The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} \overline C \,D + AB\overline C \,\overline D $$
GATE ECE 2007
8
The point p in the following figure is stuck- at-1. The output f will be GATE ECE 2006 Digital Circuits - Boolean Algebra Question 16 English
GATE ECE 2006
9
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 available, a minimum cost solution for realizing F using only 2-input NOR gates and 2-input OR gates (each having unit cost) would have a total cost
GATE ECE 2004
10
The Boolean expression AC + B$$\overline C $$ is equivalent to
GATE ECE 2004
11
If the functions W, X, Y and Z are as follows

W= R+$$\overline P Q + \overline R $$ S
X = $$X = PQ\overline R \,\overline S + \overline P \,\overline Q \,\overline R \,\overline S + P\overline Q \,\overline R \,\overline S $$
Y = $$RS + \overline {OR + P\overline Q + \overline {PQ} } $$
Z = $$R + S + \overline {PQ + \overline {PQR} + P\overline {QS} } $$


GATE ECE 2003
12
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
13
The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B\overline C + \overline A BC + AB\overline C )$$
GATE ECE 1999

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