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Logic Gates

DCS201- Computer Science

By:Dilum Bandara

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CSE 2

Outline

p Boolean algebra

p Different types of gates

p Gate networks

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CSE 3

Boolean Algebra

p George Boole (1815-1864) developed analgebra know an as the Boolean algebra

p to examine a given set of propositions

(statements) with a view to checking theirlogical consistency & simplifying them byremoving redundant statements or clauses

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CSE 4

Example

pKamal is a clever student and hepasses exams well

1 (TRUE)1 (TRUE)

0 (FALSE)0 (FALSE)

He passes exams wellKamal is a clever

student

This is a truth table

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CSE 5

Boolean Algebra cont

p AND operation is called BooleanMultiplication

n Indicated by period (.) symbol

n A.B

p OR operation is called Boolean Addition

n Indicated by plus (+) symbol

n A+B

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CSE 6

Some Boolean Algebraic Rules

p Boolean addition

0+0 = 0

0+1 = 11+0 = 1

1+1 = 1

p Boolean multiplication

0.0 = 0

0.1 = 01.0 = 0

1.1 = 1

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CSE 7

Logic Gates

p Computers are developed using bi-stabledevices such as transistors.

p They can be in only 2 states either ON orOFF.

p A simple switch is an example for such adevice witch can either be ON or OFF.

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CSE 8

Logic Gates cont

11

00

BulbSwitch

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CSE 9

Fundamental logic gates

1. AND are all inputs are true?

2. OR is at least one input is true?

3. NOT flip the truth value

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CSE 10

AND gate

111

001

010

000

LBA

L = A.B

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CSE 11

Symbol

111

001

010

000

ZBA

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CSE 12

OR Gate

111

101

110

000

ZBA

Z = A+B

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CSE 13

NOT gate

01

10

ZA

Also called the Inverter

AZ =

A+

A+

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CSE 14

Gate Networks

p The AND, OR and NOT gates can beinterconnected together to form othergates & logic networks.

p These are also called combinationalnetworks.

p Based on these fundamental gates NAND,NOR, XOR and XNOR gates are formed.

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CSE 15

NAND gate

X

01111001

1010

1000

(Z)X (A.B)BA

BAZ .=

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CSE 16

NOR Gate

011001

010

100ZBA

BZ +=

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CSE 17

XOR Gate

p Exclusive OR gate

BABAZ..

+=

011

101110

000

ZBA

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CSE 18

Logic Network - Example

pBuild the gate networkn Z = X (X+Y)

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CSE 19

A practical Scenario

p Saman will go to the party if Kamal doesnot go

p A Kamal going to the party

p Z Saman going to the party

AZ =

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CSE 20

Practical Scenario 2

pSaman will go to the party if Ranigoes and Kamal does not.

pA Kamal going to the partypB Rani going to the partypZ Saman going to the party

ABZ.

=

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CSE 21

Gate network

ANDB z

NOT

A

Kamal

SamanRani