Boolean Algebra · Digital Circuits · GATE ECE
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
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
The Boolean expression
(X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to
GATE ECE 2014 Set 1
5
For an n - variable Boolean function maximum number of prime implicants is
GATE ECE 2014 Set 2
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
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
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
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
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
Marks 4
Marks 5
1
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 operates a relay. The relay turns on when F(ABCD)=1 for the following states of the inputs (ABCD):'0000', '0010' ,0101',0110','1101' and '1110'. States '1000' and '1001' do not occur, and for the remaining states, the relay is off. Minaining states, the relay is off. Minimize F with the help of a Karnaugh map and realize it using a minimum number of 3- input NAND gates.
GATE ECE 1999
2
Its is desired to generate the following three Boolean functions.
$$\eqalign{
& {F_1} = a\,\overline b \,c + \overline a \,b\overline c + bc \cr
& {F_2} = \,a\,\overline b \,c + ab + \overline a \,b\overline c \cr
& {F_3} = \,\overline a \,\overline b \,\overline c + abc + \overline a c \cr} $$
By using an OR gate array as shown in figure where $${P_{1\,}}\,to\,{P_5}$$ are the product terms in one or more of the variables a, $$\overline a $$, b, $$\,\overline b $$, c and $$\overline c $$.
GATE ECE 1996
Marks 10
1
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 block diagram of the converter is shown in figure.
(A) draw K-map for outputs, W, X, Y, and Z.
(B) Obtain minimized expression for the outputs W, X, Y, and Z.
(A) draw K-map for outputs, W, X, Y, and Z.
(B) Obtain minimized expression for the outputs W, X, Y, and Z.
GATE ECE 1995
2
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 function in the sum of products form. Also, given the realization using only two-input NAND gates
.
GATE ECE 1991