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# Applications of Boolean Algebra

TopOne of the best applications of Boolean Algebra is to use them in the logical circuits. Basically there are three ways to represent logic. These are Truth Tables, logic circuit diagram and Boolean expression. Let’s consider two variables X and Y and design various logic gates using the concept of boolean algebra. First of all, we will design AND gate. This is formed by the Combination of a NAND and NOT gate. This is shown below.

This is the symbol for AND gate. Which has two inputs (X, Y) and one output (Z).
Boolean expression for AND gate will be given by the following expression:
Z = X. Y
Lets discuss the truth table for AND logic gate.
 Input X Input Y Output Z 0 0 0 0 1 0 1 0 0 1 1 1
Let’s discuss NAND gate. This is made from an AND gate in series with a NOT gate.
The symbol for the NAND gate is shown below.

Boolean expression for this gate is given as Z = (X.Y)'
Truth table for NAND gate is just opposite to the AND gate. When the output of the AND gate is inverted then we will get NAND gate.
 Input X Input Y Output Z 0 0 1 0 1 1 1 0 1 1 1 0

In an OR gate, if any of the inputs is one, the output will be one. The symbol and truth table for OR gate is shown below

The Boolean expression for the OR gate is
Z = X + Y
The truth table for the OR gate will be given as follows:
 Input X Input Y Output Z 0 0 0 0 1 1 1 0 1 1 1 1
The NOT gate represents an inverted output that is if the input is one, the output will be zero and
vice – versa.
The symbol of this gate will be

Here A’ is representing inverted output
 Input A Output A’ 0 1 1 0