### Logic gate

A

**logic gate**is an idealized or physical device, which implements a Boolean function. Different types of logic gates are used in different cases.Read about the truth table with example.

That is, it performs a logical operation on one or more binary inputs and produces a single binary output. It is playing a very important role in electronics.

It is a basic element. Using a lot of gates many big devices are created.

**Types of logic gate**

- Basic logic gates: AND, OR, NOT
- Universal gates: NAND, NOR
- Exclusive gates: X-OR, X-NOR
- Complex/Compound gates: AOI and OAI complex gates
- Buffer gate

### Basic logic gate

Here we are discussing

**basic logic gates**. They are AND, OR, NOT.**AND gate**

This circuit has two or more inputs and it gives produces only a single output which is the logical AND operation of all inputs. We represent this logical operation by

**.**sign.If A and B are two inputs of a logical AND gate then output X will be

X = A.B

The truth table for the AND gate of two inputs is given below.

A | B | X |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

Here, if both inputs are 1 then the output is 1. Otherwise, the output is 0.

AND gate |

AND gate is used for making a security alarm system and also in different machine security. By 0 and 1 any unique condition can be generated. That helps for securing the systems.

**OR gate**

This circuit has two or more inputs and it gives produces only a single output which is the logical OR is the operation of all inputs. We represent this logical operation by +

**sign.**If A and B are two inputs of a logical OR gate then output X will be

X = A+B

The truth table for the OR gate of two inputs is given below.

A | B | X |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

Here, if one of the inputs is 1 then we will get 1 as output.

#### NOT gate

This logical circuit has only a single input and we also get only a single output from this. The output is the inversion of the given input. This gate is also called an inverter. We represent this logical operation by the "¯"

**sign. It complements the input.**If A is the input of a logical NOT gate then output X will be

X= Ā

The truth table for NOT gate is given below.

A | X =Ā |

0 | 1 |

If the input is 0 then output is 1 and if the input is 1 then it will give 0 as output.

### Universal gates

## Universal gates are that type of gate by using that we can implement any type of Boolean functions.

A digital circuit is designed using different logic gates. But only using a single type of gate we can make the digital circuit more simply.Two types of Universal gates are

- NAND
- NOR

## We can implement any type of Boolean functions by using NAND and NOR gates. Because of this, these two gates are called the universal gates.

#### NAND

### This gate takes more than a single input and gives a single output which is the inversion of logical AND operation of those inputs.

If A and B are two inputs of a logical NAND gate then output X will be

X= A͞.B

The truth table for a NAND gate of two inputs is given below.

A | B | X |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Here, if both inputs are 1 then the output is 0. Otherwise, the output is 1.

#### NOR gate

### The Universality of NAND gate

Other logical gates are preventable by using the NAND gate.

**AND gate by using NAND gate**

AND gate by using NAND gate |

For representing AND gate by using the NAND gate we have used two NAND gates.

**OR gate by using NAND gate**

### For representing the OR gate by using the NAND gate we have used three NAND gates.

**NOT gate by using NAND gate**

**NOR gate by using NAND gate**

For representing the NOR gate by using the NAND gate we have used four NAND gates.

**X-OR gate by using NAND gate**

### For representing the X-OR gate by using the NAND gate we have used five NAND gates.

**X-NOR gate by using NAND gate**

### For representing the X-NOR gate by using the NAND gate we have used five NAND gates.

### The universality of NOR gate

Other logical gates can be designed by using the NOR gate.

**AND gate by using NOR gate**

AND gate by using NOR gate |

For representing AND gate by using the NOR gate we have used three NOR gates.

### For representing the OR gate by using the NOR gate we have used two NOR gates.

### For representing NOT gate by using the NOR gate we have used only a single NOR gate.

### For representing a NAND gate by using the NOR gate we have used 4 NOR gates.

### For representing the X-OR gate by using the NOR gate we have used 5 NOR gates.

For representing the X-NOR gate by using the NOR gate we have used 5 NOR gates.

### Exclusive gates

Two

**exclusive gates**are:- X-OR(Exclusive OR) gate
- X-NOR(Exclusive NOR) gate

#### X-OR gate

This circuit has two or more inputs and it gives produces only a single output which is the logical X-OR operation of all inputs. The output will be high when both inputs are different and will be low when inputs are the same.

We represent this logical operation by " ⊕ " sign.

If A and B are two inputs of a logical X-OR gate then output X will be-

X = A⊕B

Here,

X = ĀB+AB̄

The truth table for the X-OR gate of two inputs is given below.

A | B | X |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Here, if both inputs are 1 or both are 0 then the output is 0. Otherwise, the output is 1.

Fig: X-OR gate

#### X-NOR gate

This circuit has two or more inputs and it gives produces only a single output which is the logical X-NOR operation of all inputs. The output will be high when both inputs are the same and will be low when inputs are different.

If A and B are two inputs of a logical X-NOR gate then output X will be

Here,

X= AB+ĀB̄

A truth table for the X-NOR gate of two inputs is given below.

A | B | X |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

***Buffer gate **

In the amplifier buffer gate is used. Buffer gate does an interesting task. It amplifies the signal. For increasing propagation delay of signal buffer gate is used.

Buffer gate |

The truth table of the buffer gate

Here we will get the output as like input.

Input | Output |

0 | 0 |

1 | 1 |

**Logic gates****Types of logic gate**- Basic logic gates: AND, OR, NOT
- Universal gates: NAND gate, NOR gate, Universality of the universal gates.
- Exclusive gates: X-OR, X-NOR

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