In this lecture, we are going to learn about the Logic of the XOR Gate in every detail. We will discuss what is XOR gate, the symbol of the XOR gate, the XOR gate truth table, the XOR gate boolean expression, 3 input xor gate truth table, IC 7486 XOR gate, 7486 ic datasheet So let’s start with a basic understanding of the Logic NOR gate.

**XOR Gate**

XOR and XNOR gates are special-purpose gates. They can be used for applications such as half adder, full adder, and subtractor.

These gates are also called derived gates.

The XOR Gate is abbreviated as EX-OR gate or sometimes as Exclusive-OR gate.

An XOR gate can have two or more two inputs terminals and one output terminal.

**XOR Gate Symbol**

The XOR gate symbol is shown in the figure below.

**XOR Gate Truth Table**

The **XOR Gate Truth Table** is as shown in the figure below which shows that, when both the inputs are identical (A=B), the output is LOW (0) i.e. Y=0 for A=B=0 or A=B=1, and the output is HIGH (1) when A≠B.

**XOR Gate Boolean Expression**

The Boolean expression of a xor gate is:

\mathrm{Y = \bar A B + A \bar B}

\boxed{\mathbf{Y = A \oplus B}}

**XOR Gate Circuit Diagram**

xor gate circuit diagram is shown in the below figure. We can make the XOR gate using the basic 2 AND Gate, 2 NOT Gate, and 1 OR Gate.

**XOR Gate Using NAND Gate**

There are 4 NAND Gates required to build the XOR Gate using NAND Gate. The logic diagram of the XOR Gate using the NAND gate is shown in the below image.

**3 Input XOR Gate Truth Table**

XOR gates have more than two input and output areas available in the market.

Symbols of such XOR gates and the truth table of 3-input XOR gate and 4-input XOR gate are shown in the figure below.

This truth table shows that the output of the XOR gate is HIGH (1) if an odd number of inputs are HIGH (1).

**Boolean Expression for 3-input ****XOR gate** **and 4-input XOR gate**

**XOR gate**

The Boolean expression for a 3-input XOR gate is:

\boxed{\mathbf{Y = A \oplus B \oplus C}}

The Boolean expression for a 4-input XOR gate is:

\boxed{\mathbf{Y = A \oplus B \oplus C \oplus D}}

**Timing Diagram of XOR Gate**

Note that during intervals, I, II, and V, the input voltages are identical i.e. A = B, therefore the output Y = 0 whereas during intervals III and IV, the input voltages are not identical i.e. A ≠ B, therefore the output voltage Y= 1.

This shows that the XOR gate obeys the truth table even for the pulsed operation.

**IC 7486**

IC 7486 is the standard packaging of the XOR gate. It consists of four two-input XOR gates.

**IC 7486 Pin Diagram**

The **IC 7486 Pin Diagram** is shown in the figure below:

7486 IC Datasheet: | Click Here |

**Application of XOR gate**

Some of the applications of XOR gates are as follows:

- As a magnitude Comparator.
- In the binary-to-gray code converter.
- used in adder and subtractor circuits.
- In the parity generator.
- as a modulo-2 adder.

**Frequently Asked Questions (FAQs)**

**The expression of a xor gate is**

The Boolean expression of a xor gate is: \boxed{\mathbf{Y = A \oplus B}}

**IC 7486 is used for which logic gate?**

IC 7486 ias used for xor logic gate.

**What is an XOR logic gate?**

The simplest XOR gate is a two-input digital circuit that outputs a logical “1” if the two input values differ, i.e., its output is a logical “1” if either of its inputs are 1, but not at the same time (exclusively).

**What is the formula for XOR gate?**

**Y** **= (A’ + B’) (A + B)**

Click To know about some More Gates

AND Gate | Click Here |

OR Gate | Click Here |

NOT Gate | Click Here |

NOR Gate | Click Here |

XOR Gate | Click Here |

XNOR Gate | Click Here |

NAND Gate | Click Here |