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# What are Logic Gates?

Last updated date: 24th May 2024
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## What are Basic Logic Gates

Imagine a world where there are no computers, smartphones, or the internet. It might be tough to imagine, huh? Well, these amazing gadgets that are a big part of our daily lives rely on small but super important parts called logic gates. In this lesson, we are going to dive into the secrets of these basic pieces of digital electronics. We will look at the different kinds of logic gates, what they do, and how they're used. And don't worry, we'll explain everything in a simple and interesting way, so even the trickier ideas will become really easy to understand.

A Logic gate is a kind of the basic building block of a digital circuit having two inputs and one output. The input and output relationship is based on a certain logic. These gates are implemented using electronic switches such as diodes, transistors. But, in practice, the basic logic gates are built using CMOS technology, MOSFET(Metal Oxide Semiconductor FET), FETS. Logic gates are used in microcontrollers, microprocessors, electronic and electrical project circuits, and embedded system applications. The basic logic gates are categorized into seven types as AND, OR, XOR, NAND, NOR, XNOR, and NOT.

These are the important digital devices, mainly based on the Boolean function. Logic gates are used to carry out the logical operations on single or multiple binary inputs and result in one binary output. In simple words, logic gates are the electronic circuits in a digital system.

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### Types of Basic Logic Gates

There are various basic logic gates used to perform operations in digital systems. The common ones are given below.

• OR Gate

• AND Gate

• NOT Gate

• XOR Gate

Also, these gates can be found in a combination of one or two. Therefore we get other gates like NAND, NOR, EXOR, and EXNOR Gates.

OR Gate:

The OR gate output attains the state 1 if either one or more inputs attain the state 1.

The representation of an OR gate can be given by,

(Image will be Updated soon)

(Image will be Updated soon)

Boolean expression of OR gate can be given by,

Y = A + B,

which reads as Y equals A ‘OR’ B.

The truth table of the two-input OR basic Gate can be given as follows.

 A B Y 0 0 0 0 1 1 1 0 1 1 1 1

OR Gate Motto: "Welcome, as long as at least one of you is here."

Output: 1 if any input is 1

AND Gate:

In an AND gate, the output attains state 1 if and only if all the inputs are in state 1.

(Image will be Updated soon)

(Image will be Updated soon)

Boolean expression of AND Gate can be given by,

Y = A . B

The truth table of the two-input AND basic Gate can be given as follows.

 A B Y 0 0 0 0 1 0 1 0 0 1 1 1

AND Gate Motto: "Only if everyone agrees, I'll let you pass."

Output: 1 only if all inputs are 1

NOT Gate:

The output in a NOT Gate attains state 1 if and only if the input does not attain state 1.

The Boolean expression is

$Y = \bar{A}$

The truth table of NOT gate is given below:

 A Y 0 1 1 0

NOT Gate Motto: "I'm here to disagree and flip things around."

Output: The opposite of the input

### Basic Logic Gates

Logic Gates

Logic gates are the basic components of any digital system. Logic gates are the electrical circuit with only one output and one or more inputs. A specific logic governs the relationship between the input and the output. AND gate, OR gate, NOT gate, and so on are examples of logic gates.

A logic gate is an idealistic model of computing or a practical electronic device that implements a Boolean function, which is a logical operation that creates a single binary output from one or more binary inputs.

### Types of Logic Gates

AND Gate:

It has one output and n inputs (n >= 2).

(Image will be Updated soon)

This is the Logic Diagram of AND Gate. The AND gate has a round output and a flat input.

Truth Table-

 A B AB 0 0 0 0 1 0 1 0 0

OR Gate:

If one or more inputs reach state 1, the OR gate output will reach state 1.

Logic Diagram of OR Gate. The input side of the OR gate is curved, whereas the output side is sharply pointed.

(Image will be Updated soon)

Truth Table-

 A B A+B 0 0 0 0 1 1 1 0 1

NOT Gate:

If and only if the input does not reach state 1, the output of a NOT Gate reaches state 1. Logic Diagram of NOT Gate. A forward arrow with a little circle at the output is the NOT gate. The output is negating the input, as indicated by the circular component of the symbol.

(Image will be Updated soon)

Truth Table-

 Input Output A B 0 1 1 0

Combined Logic:

A combined logic system, also known as combinatorial logic, is created by connecting many gates together. We can utilize truth tables to match logical outputs for multiple input conditions while designing a combined logic system. The conditions in the table are used to create Boolean expressions. The phrase can then be simply converted into a logic gate diagram.

NAND Gate:

It's a digital circuit with two or more inputs that creates an output that's the logical AND of all those inputs inverted. Logic NAND Gates use digital circuits to provide the desired logical function and are given a symbol that resembles a normal AND gate with a circle, sometimes referred to as an "inversion bubble," at its output to represent the NOT gate symbol with the logical operation of the NAND gate. The NAND function, like the AND function, can have any number of independent inputs, and commercially available NAND Gate ICs come in typical 2, 3, or 4 input configurations. If more inputs are needed, the typical NAND gates can be cascaded to produce more.

Logic Diagram of NAND gate-

(Image will be Updated soon)

Truth Table-

 A B -AB 0 0 1 0 1 1 1 0 1 1 1 0

NAND Gate Motto: "I'm like AND, but I love to say no."

Output: 0 only if all inputs are 1

NOR Gate:

It's a digital circuit with two or more inputs that creates an output that's the logical OR of all those inputs inverted. Logic NOR Gates are available using digital circuits to generate the appropriate logical function and are given a symbol resembling a normal OR gate with a circle, commonly referred to as an "inversion bubble," at its output to indicate the NOT gate symbol with the logical operation of the NOR gate. The NOR function, like the OR function, can have any number of separate inputs, and commercially available NOR Gate ICs come in 2, 3, or 4 input configurations. If more inputs are needed, the typical NOR gates can be cascaded to produce more.

Logic Diagram of NOR Gate-

(Image will be Updated soon)

Truth Table-

 A B A+B (bar) 0 0 1 0 1 0 1 0 0 1 1 0

NOR Gate Motto: "Sorry, I only accept none or all."

Output: 1 only if all inputs are 0

XOR Gate:

The Exclusive-OR gate is known as the XOR gate. This gate is a unique sort of gate that can be found in a variety of computational circuits. There are two special gates, Ex-OR and Ex-NOR, in addition to the AND, OR, NOT, NAND, and NOR gates. These gates aren't basic gates in and of themselves; they're made up of other logic gates. Their Boolean output function is powerful enough to be termed a full logic gate. The hybrid gates are the XOR and XNOR gates.

Truth Table-

 A B Y 0 0 0 0 1 1 1 0 1 1 1 0

XOR Gate Motto: "I'll let you pass only if you're unique."

Output: 1 only if the inputs are different

XNOR Gate:

The Exclusive-NOR gate is known as the XNOR gate. It is a digital logic gate that outputs TRUE (1) only when both its inputs are the same, either both TRUE or both FALSE. Otherwise, it outputs FALSE (0). The XNOR gate is essentially the opposite of the XOR gate. The XOR gate outputs TRUE only when its inputs are different, whereas the XNOR gate outputs TRUE only when its inputs are the same.

Truth Table-

 A B C 0 0 1 0 1 0 1 0 0 1 1 1

XNOR Gate Motto: "I'm here to celebrate perfect agreement."

Output: 1 only if the inputs are the same

## Application of Logic Gates

Logic gates are like electronic building blocks that do specific jobs. They're used in many things, like:

• Computers (processors, memory)

• Smartphones

• Calculators

• TVs

• Digital cameras

• Industrial machinery

• Medical equipment

• And many more!

These gates follow certain rules or truth tables.

The cool thing is, that you can use these basic gates together to do more complicated stuff. There's no strict limit to how many gates you can use, but it depends on the space in the device. In digital circuits, you'll often see a bunch of these gates working together.

## De Morgan’s Theorem

De Morgan's Theorem is like a ninja trick for dealing with logic puzzles. Basically, the theorem says that you can get the same result by doing the opposite operation and switching the true and false values.

Let's simplify it with two easy rules:

First Theorem: The negation of a conjunction (AND) is equivalent to the disjunction (OR) of the negations.

$(\bar{A \cdot B}) = \bar{A} + \bar{B}$

Second Theorem: The negation of a disjunction (OR) is equivalent to the conjunction (AND) of the negations.

$(\bar{A + B}) = \bar{A} \cdot \bar{B}$

## Conclusion:

In the world of electronics, think of logic gates as the traffic controllers of information. They manage how signals move and are like the essential building blocks of digital circuits. Picture them as tiny decision-makers that handle binary inputs (0 or 1) and give one binary output following a specific rule. Understanding these logic gates is really important for doing well in JEE Main, as they form the basis for various ideas in electronics, computer science, and communication systems. So, mastering them is key to success in these fields.

## FAQs on What are Logic Gates?

1. Explain the NAND and NOR Gates, with their Respective Truth Tables?

NAND Gate

The NAND Gate is formed with the combination of ‘AND’ and ‘NOT’ Gate.

The Boolean expression of NAND Gate is given as below:

Y′ = A￣. B

 A B Y′ = A￣. B Y 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0

NOR Gate

NOR Gate can be formed by the combination of OR and NOT gates.

Boolean expression of NOR Gate is given below.

Y′ = A￣+ B

The truth table of a NOR gate can be given as below.

 A B Y′ = A￣+ B Y 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0

2. Explain the XOR and XNOR Gates?

XOR Gate

The XOR Gate forms with a combination of NOT, AND, and OR gates.

The logic gate gives results output (i.e., 1) if either input A or B but not both are high (i.e., 1) is known to be an XOR gate or the exclusive OR Gate. It can be noted that if both XOR gate inputs are high, the output is low (i.e., 0).

Boolean expression of the XOR gate can be given by,

Y = A ⊕ B

The truth table of the XOR gate can be given as follows.

 A B Y 0 0 0 0 1 1 1 0 1 1 1 0

Exclusive NOR Gate

The exclusive NOR gate is otherwise known as the XNOR gate. It is the combination of XOR and NOT gates.

Boolean expression of an XNOR gate can be given by,

Y = A ⊙ = AB + AB

3. Why do we need the Logic Gates?

Burglar alarms and buzzers both use NAND Gates. They are mostly employed in calculation and processing circuits. They're also found in push-button controls. Consider the example of a doorbell. They are required for the proper operation of street lights. The data transfer function is enabled or inhibited using AND Gates. TTL(Transistor-Transistor Logic) and CMOS circuitry also employ them. Boolean Algebra is used to execute logical operations, making circuit design more cost-effective and straightforward. It's easy to tell the difference between logic '1' and logic '0.'.

4. What are the basic types of logic gates?

The basic types of logic gates are:

1. AND gate: Outputs a high (1) only if both inputs are high.

2. OR gate: Outputs a high if at least one input is high.

3. NOT gate (Inverter): Inverts the input, producing a low output for a high input and vice versa.

4. NAND gate: The inverse of the AND gate, outputting a low only when both inputs are high.

5. NOR gate: The inverse of the OR gate, outputting a high only when both inputs are low.

6. XOR gate (Exclusive OR): Outputs a high if the inputs are different, and a low if they are the same.

7. XNOR gate (Exclusive NOR): Outputs a high if the inputs are the same, and a low if they are different.

5. What are universal logic gates?

NAND and NOR gates are considered universal because they can be combined to create any other logic gate, making them essential for building complex digital circuits.

6. What are some important facts about logic gates?

• Logic gates operate on binary signals, representing either a 0 (low) or 1 (high) voltage level.

• They are typically implemented using electronic components like transistors or diodes.

• Logic gates can be combined to create more complex circuits with intricate logic functions.

• The delay time of a logic gate, the time it takes for the output to change after an input change, is a crucial factor in circuit design.