# Logic Gates (OR, AND, NOT, NOR, NAND, XOR, XNOR) Truth Table

Logic Gates are defined as digital circuits that operates on one or more digital inputs and produces an one output signal. Logic gates are called digital circuits because the input and output signals are either lower voltage(0) or high voltage(1).

These are also called logic circuits because they can be easily analysed by Boolean algebra.

Logic Gates can be divided into two types:

- Basic gates
- Derived gates

## Basic Gates

Basic gates are defined as gates very basic and are not complicated. These are of three types

- AND gate
- OR Gate
- NOT Gate

## Derived Gates

Daraind Gates are those gets which are made of combination of basic Gates. These are of four types:

- XOR Gate
- NOR Gate
- XNOR Gate
- NAND Gate

Let us discuss all the gates one by one.

## Basic Gates

### AND Gate

The AND gate is a logic circuit which has two or more inputs and one single output. The AND Gate will produce output 1 only when both the inputs are 1. If there is any 0 in the input the output will be 0.

#### Logic Symbol of AND Gate

Logic Symbol for AND gate is given below:

Input | Input | Output |

A | B | Y |

0 | 1 | 0 |

1 | 0 | 0 |

0 | 0 | 0 |

1 | 1 | 1 |

#### Truth Table for AND Gate

The And gate performs the operation on the basis of simply multiplication and multiplication is also known as the AND function. The output of the AND gate is given by

Y= A.B

Where dot ‘.’ represent the AND logic.

Here, A and B denotes the inputs. The output is given by Y. The total number of possible

combinations in the truth table is determined by

the following formula:

N= 2^{n}

where: ‘N’ is the total number of possible

combinations in AND Gate

‘n’ is the total number of input variables

### OR Gate

The OR Gate is a logic circuit which gives ‘1’ output if any of the input is ‘1’. If there are both inputs are ‘0’ then the output will be ‘0’. The OR gate performs the basic operation of addition as that multiplication in AND gate. The algebraic or mathematical expression for the output of the OR gate is given as

Here, A and B denotes the inputs. The output is given by Y. The total number of possible

combinations in the truth table is determined by

the following formula:

N= 2^{n}

where: ‘N’ is the total number of possible

combinations in AND Gate

‘n’ is the total number of input variables.

#### Logic Symbol of OR Gate

The Logic Symbol for OR gate is given below:

Input | Input | Output |

A | B | Y |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

#### Truth Table for OR Gate

### NOT Gate

NOT gate is the simplest logic circuit. It performs the inversion operation which means to make output state opposite to the input state i.e. if ‘1’ is given as input, then ‘0’ will be the output and if ‘0’ is given as input, then ‘1’ will be the output.

Only two input combinations are possible in NOT gate. Either 0 or 1.

#### Logic Symbol of NOT Gate

#### Truth Table for NOT Gate

Input | Output |

A | Y |

0 | 1 |

1 | 0 |

## Derived Gates

### XOR Gate (Exclusive-OR Gate)

The XOR Gate is not so common but it is very important and used in many applications. XOR Gate is also called as exclusive-OR gate.It has two or more input signals but one output signal. It is different from OR gate.

XOR gate produces the output ‘1’ only when the input combinations have odd number of ‘1’. The output is 0 when there are even number of 1’s in the input. The output is 1 when there are odd number of 1’s in the input.

It is written as

Y = A ϴ B

#### Logic Symbol of XOR Gate

The logic Symbol for XOR gate is given below

Input | Input | Output |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

#### Truth Table for XOR Gate

### NOR Gate

NOR gate is a combination of NOT and OR gate. NOR gate is complement of XOR gate.

Output of NOR gate will be 1 only when all inputs are 0 and output will be 0 if any input represents a 1 .

#### Logic Symbol of NOR Gate

The Logic Symbol of NOR Gate is given as

#### Truth Table for NOR gate

Input | Input | Output |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

### XNOR Gate

The XNOR gate is the complement of the XOR gate. The output of the XNOR Gate is 1 only when the logic values of both A and B is same i.e. either both are equal to 1 or both are 0. The XNOR output is 0 when its inputs are different.

#### Logic Symbol for XNOR Gate

The Logic Symbol for XNOR Gate is

Truth Table for XNOR Gate

Input | Input | Output |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

### NAND Gate

A NAND gate has the two or more input signal but has only one output signal. The NAND gate is the complemented of the AND gate. The output of NAND gate will be 0 only when all inputs are 1 and output will be 0 if any input represents a 0. NAND is the short form of the NOT-AND.

#### Logic Symbol for NAND Gate

The Logic table for NAND gate is as below

#### Truth Table for NAND Gate

Input | Input | Output |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

## FAQ

### What are Logic Gates?

Logic Gates are defined as digital circuits that operates on one or more digital inputs and produces an one output signal. Logic gates are called digital circuits.

Also read about Basic Electrical Tools

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