boolean algebra

The digital circuit shown has 3 inputs (x, y, and z). The simplified logical expression for the output (OUT) is:

A Boolean function is given as $$ f=(\bar{u}+\bar{v}+\bar{w}+\bar{x}) \cdot(\bar{u}+\bar{v}+\bar{w}+x) \cdot(\bar{u}+v+\bar{w}+\bar{x}) \cdot(\bar{u}+v+\bar{w}+x) $$ The simplified...

Simplified form of the Boolean function $F(P,Q,R,S) = \overline{P}\overline{Q} + \overline{P}QS + \overline{P}Q\overline{R}\overline{S} + P\overline{Q}\overline{R}\overline{S}$ is

Simplified form of the Boolean function $$ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S} $$ is

The output expression for the Karnaugh map shown below is

For a 3-input logic circuit shown below, the output Z can be expressed as

The Boolean expression AB + AC + BC simplifies to

The output expression for the Karnaugh map shown below is

The Boolean expression $$AB + A\overline C + BC$$ simplifies to

Consider the following Sum of products expression, $$F.$$ $$F = ABC + \overline A \overline B C + A\overline B C + \overline A BC + \overline A \overline B \overline C $$ The equiv...

The $$SOP$$ (sum of products) from of a Boolean function is $$\sum \left( {0,1,3,7,11} \right),$$ where inputs are $$A,B,C,D$$ ($$A$$ is $$MSB$$, and $$D$$ is $$LSB$$). The equival...

The simplified form of the Boolean expression $$Y = \left( {\overline A BC + D} \right)\left( {\overline A D + \overline B \overline C } \right)$$ can be written as

The Boolean expression $$X\overline Y Z + XYZ + \overline X Y\overline Z + \overline X \overline Y Z + XY\overline Z $$ can be simplified to

The logic function $$f = \overline {\left( {x.\overline y } \right) + \left( {\overline x .y} \right)} $$ is the same as

In a digital combinational circuit with $$4$$ inputs $$(A, B, C, D),$$ it is required to obtain an output of logical $$1$$ only for the input combination $$(A = 1; B = C = D = 0).$...