DGE1 - Introduction to Boolean Algebra PDF

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Introduction to Boolean Algebra...

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UNIT - 1

INTRODUCTION TO BOOLEAN ALGEBRA

Topics Covered  What is Boolean Algebra  Boolean Variable / Logic Variable  Truth Table  Logic Representation

Boolean Algebra Boolean Algebra is a branch of algebra which deals with only two quantities zero (0) and one (1). It was introduced by english mathematician Sir George Boole in 1854. It is used to design and analyze digital circuits like traffic signals, assembly line, manufacturing line, robots, automation, computer circuit, smartphone, microwave ovens, washing machine, digital clock and other digital equipments.

( 1815 – 1864 )

Boolean Variable A Boolean variable or logical variable is a container which can hold only two quantities either 0 or 1. It can have only two states like ( 0 / 1 ), (False / True ), (Low/High), (Off/On) Example – If A is boolean variable then two states of it is represented as A and A’ If A = 0 then A’= 1 | If A = 1 then A’ = 0 |

If A = false then A’= true If A = true then A’ = false

Truth Table Truth Table is a tabular representation which contains all possible combination of all standard inputs and respective standard outputs. Example –

INPUT

A/C

SW-A

SW-B

OFF - 0

OFF - 0

0

OUTPUT (Y)

INPUT

A 0

B 0

OUTPUT Y 0

Truth Table Truth Table is a tabular representation which contains all possible combination of all standard inputs and respective standard outputs. Example –

INPUT

A/C

SW-A

SW-B

OFF - 0

ON - 1

0

OUTPUT (Y)

INPUT

A 0 0

B 0 1

OUTPUT Y 0 0

Truth Table Truth Table is a tabular representation which contains all possible combination of all standard inputs and respective standard outputs. Example –

INPUT

A/C

SW-A

SW-B

ON - 1

OFF - 0

0

OUTPUT (Y)

INPUT

A 0 0 1

B 0 1 0

OUTPUT Y 0 0 1

Truth Table Truth Table is a tabular representation which contains all possible combination of all standard inputs and respective standard outputs. Example –

INPUT

A/C

SW-A

SW-B

ON - 1

ON - 1

1

OUTPUT (Y)

INPUT

A 0 0 1 1

B 0 1 0 1

OUTPUT Y 0 0 0 1

Logic Representation There are two types of logic representation used in digital system. a) Positive Logic b) Negative Logic a) Positive Logic – In digital system positive logic represents bit 1 as true/high/on and 0 as false/low/off. Example : -

If True then A = 1 and If False then A’= 0

b) Negative Logic – In digital system negative logic represents bit 0 as true/high/on and 1 as false/low/off. Example : -

If True then A = 0 and If False A = 1

Solve @ Study Desk Define Boolean Algebra and Its application What is logic variable? What do you mean by truth table? How positive logic and negative logic differ from each other?

Thank You!

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