Introduction

Logic gates are the building blocks of any digital circuit which is the building block of modern digital systems.

A Logic gate has one or more inputs and only one output.

A logic gate is defined as an

electronic circuit

or device which makes logical decisions.

The logic gates

AND

,

OR

, and

NOT

are referred to as

Basic Logic Gates

.

The basic gates combine to form more complex logic circuits called

Combinational Logic Gates.

The available combinational logic gates are:

NAND

,

NOR

,

XOR

, and

XNOR

.

**Logic States**

In digital systems there are only two possible states represented by two voltage levels.

The two states or voltage-levels are:

HIGH and it represents Closed switches,Lights ON, or Logic-1.

LOW and it represents Open switches, Lights OFF, or Logic-0.

Basic Logic Gates

The three basic logic gates are:

1) AND

2) OR

3) NOT

**Series Switching Circuit**

Such a series switching circuit is also known as AND Switching Circuit because the lamp is

ON

only if both,

S1

AND

S2

are CLOSED.

AND Logic Gate

The digital circuit which can act exactly like an AND switching circuit is

known as AND logic gate.

Logic Symbol

The AND logic gate can have a maximum number of 8-inputs but

only

one output.

Logic Operation and Truth Table

Boolean Expression

X

=

A

AND

B

X

=

A

B

X

=

A

B

Parallel Switching Circuit

What is the number of all possible combinations for 2-input logic gate ?

Parallel Switching Circuit

Parallel Switching Circuit Operation

Such a parallel switching circuit is also known as

OR Switching Circuit

because the lamp is ON if

S1

OR

S2

OR

both are CLOSED.

OR Logic Gate

The digital circuit which can act exactly like an OR switching circuit is known as OR logic gate.

Logic Symbol

The OR logic gate can

have a maximum number of 8-inputs but only one output.

Logic Operation and Truth Table

OR Boolean Expression

X

=

A

OR

B

X

=

A

+

B

Inverter Switching Circuit

Inverter Circuit Operation

Such an Inverting Switching circuit is also known as

NOT Circuit

because the lamp is

ON

if

S

is

NOT

closed.

NOT Logic Gate

The digital circuit which can act exactly like a

NOT

switching circuit is known as

NOT

logic gate.

Logic Symbol

The NOT gate, unlike other gates, has only one input.

Boolean Expression

X

=

NOT

A

Timing Diagram

**Universal Logic Gates**

**The NAND Gate**

It is called a universal gate because it can be used to construct all basic gates or any combination of these gates.

Logic Symbol

The term

NAND

is a short form of

N

OT-

AND

. It means an AND function with inverted output.

Logic Operation and Truth Table

Boolean Expression

**The NOR Gate**

Logic Symbol

The term

NOR

is a short form of

N

OT-

OR

and is equivalent to an OR function with inverted output.

Logical Operation and Truth Table

Boolean Expression

XOR gate is made of the combination of AND, OR, and NOT gates

Logic Circuit and Symbol

The Exclusive-OR (XOR)

Logical Operation and Truth Table

Note that the XOR gate has only two inputs.

Boolean Expression

Logic Circuit

The Exclusive-NOR (XNOR)

Symbol

Logical Operation and Truth Table

The XNOR gate has only two inputs.

Boolean Expression

The bubble on the output indicates that its output is opposite that of the XOR gate.