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
The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is
GATE ECE 1998
13
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
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
The Boolean expression AC + B$$\overline C $$ is equivalent to
GATE ECE 2004
10
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
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