# Digital Logic Gates Tutorial

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Category: Education

## Presentation Description

This Presentation covers the basics of digital logic gates with animations including truth tables, symbols.

## Presentation Transcript

### PowerPoint Presentation:

DIGITAL LOGIC GATES Kulwinder Singh Lecturer ECE S. R. S. GPCG Ludhiana 1

### What is a Digital Logic Gate?:

What is a Digital Logic Gate? A logic gate performs a logical operation on one or more logic inputs and produces a single logic output. The logic normally performed is Boolean logic 2

### TERMS USED:

TERMS USED “ HIGH ” denotes a higher voltage level among the two voltage levels used to represent binary. Sometimes term “ TRUE ” or “ 1 ” is also used in place of “ HIGH ” 3

### PowerPoint Presentation:

TERMS USED “ LOW ” denotes a lower voltage level among the two voltage levels used to represent binary. Sometimes term “ FALSE ” or “ 0 ” is also used in place of “ LOW ” 4

### TRUTH TABLE:

TRUTH TABLE A truth table shows how a logic circuit's output responds to various combinations of the inputs, using logic 1 for true and logic 0 for false 5

### What We Shall Cover?:

What We Shall Cover? Definition of Gate Boolean Equation of Gate Symbol of Gate Truth Table of Gate Simulation of Gate 6

### NOT Gate:

NOT Gate The NOT gate performs the basic logical function called inversion or 1’s complement. NOT gate is also called inverter. It has one input and one output. 7

### NOT Gate contd..:

NOT Gate contd.. The purpose of this gate is to convert one logic level into the opposite logic level. When a HIGH level is applied to an inverter, a LOW level appears on its output and vice versa. 8

### NOT Gate contd..:

NOT Gate contd.. If A is the input, then output Y can be represented mathematically as F = X', Here apostrophe (') denotes the NOT (inversion) operation. 9

### NOT Gate contd..:

NOT Gate contd.. There are a couple of other ways to represent inversion, Y= !A, here ! represents inversion. Y=Ā 10

### NOT Gate Symbol:

NOT Gate Symbol Common Symbol IEEE Symbol 1 A=Input A=Input Y=Output Y=Output 11

### Equation of NOT Gate:

Equation of NOT Gate OUTPUT= NOT (INPUT) Y= NOT(A) Y= Ā 12

### TRUTH Table of NOT Gate:

TRUTH Table of NOT Gate INPUT A OUTPUT Y HIGH (1) LOW (0) LOW (0) HIGH (1) 13

### Equivalent Circuit of NOT Gate:

Equivalent Circuit of NOT Gate 14

### PowerPoint Presentation:

NOT GATE A = HIGH LOW 15

### AND Gate:

AND Gate The AND gate performs logical multiplication, commonly known as AND function. The AND gate has two or more inputs and single output. 16

### AND Gate Contd..:

AND Gate Contd.. The output of AND gate is HIGH only when all its inputs are HIGH (i.e. even if one input is LOW, Output will be LOW). 17

### AND Gate Contd..:

AND Gate Contd.. If A and B are two inputs, then output Y can be represented mathematically as Y = A.B, Here dot (.) denotes the AND operation 18

### Symbol of AND Gate:

Symbol of AND Gate Common Symbol IEEE Symbol A=Input B=Input Y= Output & A=Input B=Input Y= Output 19

### Truth Table of AND Gate:

Truth Table of AND Gate Input A Input B Output Y LOW (0) LOW (0) LOW (0) LOW (0) HIGH (1) LOW (0) HIGH (1) LOW (0) LOW (0) HIGH (1) HIGH (1) HIGH (1) Y = A . B Y= 0 * 0 = 0 Y = A . B Y= 0 * 1 = 0 Y = A . B Y= 1 * 0 = 0 Y = A . B Y= 1 * 1 = 1 20

### AND GATE:

AND GATE A = B = HIGH HIGH LOW LOW 21

### OR Gate:

OR Gate The OR gate performs logical addition, commonly known as OR function. The OR gate has two or more inputs and single output. 22

### OR Gate Contd..:

OR Gate Contd.. The output of OR gate is HIGH only when any one of its inputs are HIGH (i.e. even if one input is HIGH, Output will be HIGH). 23

### OR Gate Contd..:

OR Gate Contd.. If X and Y are two inputs, then output F can be represented mathematically as F = X+Y Here plus sign (+) denotes the OR operation. 24

### PowerPoint Presentation:

Symbol of OR Gate Common Symbol IEEE Symbol A=Input B=Input Y= Output ≥ 1 A=Input B=Input Y= Output 25

### PowerPoint Presentation:

Truth Table of OR Gate Input A Input B Output Y LOW (0) LOW (0) LOW (0) LOW (0) HIGH (1) HIGH (1) HIGH (1) LOW (0) HIGH (1) HIGH (1) HIGH (1) HIGH (1) Y = A + B Y= 1 + 1 = 1 Y = A + B Y= 1 + 0 = 1 Y = A + B Y= 0 + 1 = 1 Y = A + B Y= 0 + 0 = 0 26

### PowerPoint Presentation:

OR GATE A = B = HIGH HIGH LOW LOW 27

### NAND Gate:

NAND Gate NAND gate is a cascade of AND gate and NOT gate. This gate performs 1’s complement of AND operation of inputs. It has two or more inputs and only one output. 28

### NAND Gate contd..:

NAND Gate contd.. The output of NAND gate is HIGH when any one of its input is LOW (i.e. even if one input is LOW, Output will be HIGH). 29

### NAND Gate contd..:

NAND Gate contd.. If A and B are two inputs, then output Y can be represented mathematically as Y = (A.B)', Here dot (.) denotes the AND operation and (') denotes inversion. Or as 30

### PowerPoint Presentation:

Symbol of NAND Gate Common Symbol IEEE Symbol A=Input B=Input Y= Output & A=Input B=Input Y= Output 31

### PowerPoint Presentation:

Truth Table of NAND Gate Input A Input B Output Y LOW (0) LOW (0) HIGH (1) LOW (0) HIGH (1) HIGH (1) HIGH (1) LOW (0) HIGH (1) HIGH (1) HIGH (1) LOW (0) 32

### PowerPoint Presentation:

NAND GATE A = B = HIGH HIGH LOW LOW 33

### NOR Gate:

NOR Gate NOR gate is a cascade of OR gate and NOT gate. It performs 1’s complement of OR gate’s output. It has two or more inputs and only one output. 34

### NOR Gate contd..:

NOR Gate contd.. The output of NOR gate is HIGH when all of its inputs are LOW i.e. even if one input is HIGH, output will be LOW. 35

### NOR Gate contd..:

NOR Gate contd.. If X and Y are two inputs, then output F can be represented mathematically as F = (X+Y)’ here plus (+) denotes the OR operation and (') denotes inversion. Or as 36

### PowerPoint Presentation:

Symbol of NOR Gate Common Symbol IEEE Symbol A=Input B=Input Y= Output ≥ 1 A=Input B=Input Y= Output 37

### PowerPoint Presentation:

Truth Table of NOR Gate Input A Input B Output Y LOW (0) LOW (0) HIGH (1) LOW (0) HIGH (1) LOW (0) HIGH (1) LOW (0) LOW (0) HIGH (1) HIGH (1) LOW (0) 38

### PowerPoint Presentation:

NOR GATE A = B = HIGH HIGH LOW LOW 39

### XOR Gate:

XOR Gate An Exclusive-OR (XOR) gate is gate with two or three or more inputs and one output. The output of a two-input XOR gate assumes a HIGH state if one and only one input assumes a HIGH state. 40

### XOR Gate contd..:

XOR Gate contd.. This is equivalent to saying that the output is HIGH if either input A or input B is HIGH exclusively, and LOW when both are 1 or 0 simultaneously. 41

### XOR Gate contd..:

XOR Gate contd.. If A and B are two inputs, then output Y can be represented mathematically as OR Here denotes the XOR operation. 42

### Symbol of XOR Gate:

Symbol of XOR Gate Common Symbol IEEE Symbol A=Input B=Input Y=Output = 1 Y=Output A=Input B=Input 43

### PowerPoint Presentation:

Truth Table of XOR Gate Input A Input B Output Y LOW (0) LOW (0) LOW (0) LOW (0) HIGH (1) HIGH (1) HIGH (1) LOW (0) HIGH (1) HIGH (1) HIGH (1) LOW (0) 44

### PowerPoint Presentation:

EX-OR GATE A = B = HIGH HIGH LOW LOW 45

### XNOR Gate:

XNOR Gate An Exclusive-NOR (XNOR) gate is gate with two or three or more inputs and one output. The output of a two-input XNOR gate assumes a HIGH state if all the inputs assumes same state. 46

### XNOR Gate Contd..:

XNOR Gate Contd.. This is equivalent to saying that the output is HIGH if both input A and input B are HIGH exclusively Or input A and input B are LOW exclusively, and LOW when both are not same. 47

### XNOR Gate Contd..:

XNOR Gate Contd.. If A and B are two inputs, then output Y can be represented mathematically as Here A B denotes the XNOR operation. A B 48

### PowerPoint Presentation:

Symbol of XOR Gate Common Symbol IEEE Symbol A=Input B=Input Y=Output = 1 Y=Output A=Input B=Input 49

### PowerPoint Presentation:

Truth Table of XNOR Gate Input A Input B Output Y LOW (0) LOW (0) HIGH (1) LOW (0) HIGH (1) LOW (0) HIGH (1) LOW (0) LOW (0) HIGH (1) HIGH (1) HIGH (1) 50

### PowerPoint Presentation:

EX-NOR GATE A = B = HIGH HIGH LOW LOW 51