Boolean Algebra

A 3-input majority logic gate has inputs X, Y, and Z. The output F of the gate is logic '1' if two or more of the inputs are logic '1'. The output F is logic '0' if two or more of...

In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

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

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.\over...

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

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...

A 3-input majority gate is defined by the logic function M (a,b,c) = ab+bc+ca. Which one of the following gates is represented by the function M$$\left( {\overline {M\left( {a,b,c}...

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

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,$...

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

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

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

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...

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

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

The minimum number of NAND gates required to implement the Boolean function $$A + A\overline B $$ $$ + A\overline B C$$ is equal to

The minimum number of 2-input NAND gates required to implement the Boolean function Z=A$$\overline {B\,} $$C, assuming that A, B and C are available, is

The Boolean function A+BC is a reduced form of

For the identity AB+$$\overline A $$ C + BC= AB + $$\overline A $$ C, The dual form is

Minimum number of 2-input NAND gates required to implement the function, f=($$\overline X $$+$$\overline Y $$)(Z+W) is

Implement the function $$F=\left(\overline A+\overline B\right)\left(\overline C+\overline D\right)$$ using two open collector TTL 2-input NAND gates.