Digital Logic Gates Tutorial

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

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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

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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

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

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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

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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

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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

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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

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