Binary Number System

Binary Decimal Conversion

Octal Decimal Conversion

Hexadecimal Decimal Conversion

Binary Octal Conversion

Binary Hexadecimal Conversion

Binary Arithmetic

Binary Addition

Binary Subtraction

Binary Multiplication

Binary Division

Binary Coded Decimal

Gray Code

Alphanumeric codes

1′s Complement

2′s Complement

Hamming Code

9s and 10s Complement

De Morgan's Theorem

Logical OR Operation

Logical AND Operation

Truth Table

Logical OR Gate

Exclusive OR Gate

Logical AND Gate

NAND Gate

NOT Gate

Boolean Algebra

Excess 3 code Addition & Subtraction

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**Exclusive OR gate**is one of them. As the name suggest it is a modified version of OR gate, but how much different it is from the fundamental gate what is the difference we will know it in this article.

The **Exclusive OR gate** is a two input one output gate. The symbol and the truth table are given below.

A | B | Y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

As seen from the truth table we can see that for two input **Ex-OR gate** the combination of total input sequence are four and if we thoroughly examine the result of the truth table we can find the obvious relation of it with the truth table of OR gate. The only difference between this truth table is that in this case the output is 0 when both the inputs are same and in all the other cases the output is 1.

The mathematical representation of the operation of the Exclusive OR gate is like.

Y = ( A ⊕ B ) = A’B + AB’ (where A’ is the complement of A and B’ is the complement of B)

### Application

#### Addition

The main application of the Exclusive OR gate is in the operation of half and full adder. If we look at the truth table carefully we will find that the first three results are totally satisfying the process of binary addition but in the last input sequence i.e. when both the inputs are 1 the result according to the rule of addition should be 0 with a carry 1. In the truth table we are getting the desired 0 but a missing 1. To solve this problem during designing the circuit of an adder an AND gate is added to the **Ex-OR gate** in parallel. We will show the circuit of the adder in detail.

From the above diagram, we can see that in the circuit of a half adder the two inputs are going through an Exclusive-OR gate and through an AND gate parallelly. And with this circuit’s operation we get the total process of binary addition smoothly.

Pseudo-random number generation

To model a linear feedback shift register Ex-OR gates are used and they generate random sequence of bits.

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