Introduction to Logic Gates

Logic gates are the fundamental components of digital electronics. They are electronic circuits that perform logical operations on one or more input signals and produce a single output. These inputs and outputs are usually represented in binary form, where 0 means LOW (false) and 1 means HIGH (true).

Logic gates are used to process information and make decisions in digital systems such as computers, calculators, and other electronic devices. Each logic gate follows a specific rule or logic to determine its output based on the given inputs. There are seven basic logic gates: AND, OR, XOR,
NOT, NAND, NOR, and XNOR.

Definition of Truth Table

A truth table is a table that shows all possible combinations of input values and their corresponding outputs in a logic circuit. It helps to clearly understand how a logic gate or digital system works for every possible input condition.

Inverter (NOT Gate)

An inverter, also called a NOT gate, is a type of logic gate that takes only one input and produces one output. The output is always the opposite of the input value in the circuit. If the input is true (1), the output becomes false (0), and if the input is false (0), the output becomes true (1).

OR Gate :

An OR gate is a basic digital logic gate used in electronics. It produces a HIGH (1) output when any one or more of its inputs are HIGH (1). It produces a LOW (0) output only when all of its inputs are LOW (0). It is commonly used in digital circuits to perform logical addition.

AND GATE:

An AND gate is a basic digital logic gate used in electronics. It produces a HIGH (1) output only when all of its inputs are HIGH (1). It produces a LOW (0) output if any one or more inputs are LOW (0). It is commonly used in digital circuits to perform logical multiplication.

NOR GATE:

A NOR gate is a basic digital logic gate used in electronics. It produces a HIGH (1) output only when all of its inputs are LOW (0). It produces a LOW (0) output if any one or more inputs are HIGH (1). It performs the reverse operation of an OR gate and is formed by combining an OR gate with a NOT gate.

NAND GATE:

A NAND gate is a basic digital logic gate used in electronics. It produces a LOW (0) output only when all of its inputs are HIGH (1). It produces a HIGH (1) output when any one or more inputs are LOW (0). It performs the reverse operation of an AND gate and is formed by combining an AND gate with a NOT gate.

Special Gates

Special Gates are digital logic gates that are formed by combining basic logic gates (AND, OR, and NOT) and perform more complex or specific logical operations. These gates are not considered basic gates but are widely used in digital circuits for particular purposes. Common examples of special gates include XOR (EX-OR) and XNOR (EX-NOR) gates.

XOR (EX-OR) OR Exclusive OR GATE

An EX-OR (Exclusive OR) gate is a digital logic gate used in electronics. It produces a HIGH (1) output when the inputs are different (i.e., one is HIGH and the other is LOW). It produces a LOW (0) output when both inputs are the same (both LOW or both HIGH). In other words, it gives a HIGH output only when an odd number of inputs are HIGH. The XOR gate can be formed by combining AND, OR, and NOT gates.

The Boolean expression for a two-input EX-OR (XOR) gate with inputs A and B is:

Y=A‘B+AB‘

EX-NOR (Exclusive NOR)

An EX-NOR (Exclusive NOR) gate is a digital logic gate that produces a HIGH (1) output when all of its inputs are the same (either all LOW or all HIGH). It produces a LOW (0) output when the inputs are different. In other words, it performs the complement (inverse) of the EX-OR (XOR) gate and is also known as an equivalence gate because it checks whether the inputs are equal.

Demorgon’s theorem:

DeMorgan’s Theorem is a powerful theorem in Boolean algebra that has a set of two rules or laws. These two laws were developed to show the relationship between the two variables AND, OR, and NOT operations.

Demorgon’s first theorem:

DeMorgan’s First Law states that the complement of a sum of variables is equal to the product of their complements. In other words, the complement of two or more ORed variables is equivalent to the AND of the complements of each of the individual variables, i.e.,

(A+B)^′=A^′⋅B^′  

Logic diagram implementations of De Morgan’s first law

Demorgon’s second theorem:

DeMorgan’s second law states that the complement of the product of variables is equivalent to the sum of their individual complements.

(AB)^‘  = A^‘ +B^‘ 

Introduction of Universal Gates

In digital electronics, universal gates are special types of logic gates that can be used to design and implement any Boolean expression or digital circuit. A gate is called universal because it alone is sufficient to perform all basic logical operations, such as AND, OR, and NOT.

Types of Universal Gates

There are two universal gates:

1. NAND Gate
2. NOR Gate

Implementation of AND Gate using Universal Gates(NAND)

A NAND gate is called a universal gate because it can be used to create all other basic logic gates, like AND, OR, and NOT. This means any digital circuit can be built using only NAND gates without needing other types of gates. Hence, the NAND gate is called universal since it alone can perform all logical operations.

Applications of Universal Gates (NAND and NOR):

Universal gates like NAND and NOR are widely used in digital electronics because they can build any type of logic circuit.

• They are used to design basic logic gates such as AND, OR, and NOT.
• They help in building complex digital circuits like adders, multiplexers, and decoders.
• They are used in memory devices such as flip-flops and registers.
• They are important in computer processors and digital systems.
• They simplify circuit design by using only one type of gate.

Hence, universal gates are very useful in designing and implementing all kinds of digital systems.

Compiled By Er. Basant Kumar Yadav