Boolean Functions

 Boolean Capabilities Essay

Lecture two Boolean Capabilities

Lecture 2

Basic Boolean functions, reasoning gates and

Karnaugh maps

ITP3902 Under the radar Mathematics & Statistics

Site 1

Address 2 Boolean Functions

Logic gates

• Logic gates are digital electronic circuits in which there are only two possible says at any point, just like

• Open or close;

• Hollywood or low voltage

• A certain sign is present or absent, etc .

• Both possible says are called 1 or 0.

• The two says can be used to stand for logic beliefs. We work with 1 to represent T(rue) and 0 to represent F(alse).

• The two declares can also be used to symbolize one binary digit (bit).

ITP3902 Discrete Mathematics & Statistics

Page 2

Address 2 Boolean Functions

Logic gates: OR PERHAPS gates

• An OR gate allows two advices and produce an output according to the following truth table.

Input

Output

A

N

A+B

0

0

0

0

you

1

1

0

one particular

1

1

1

• The digital circuit symbol is

• The Boolean symbol is " +”, i. at the. Q sama dengan A + B.

ITP3902 Discrete Math & Stats

Page three or more

Lecture 2 Boolean Capabilities

Logic entrances: AND entrance

• An AND door accepts two inputs and produce an output

based on the following fact table.

Input

Output

A

B

Aпѓ—B

0

0

0

0

1

0

1

zero

0

one particular

1

1

• The electronic circuit symbol is definitely

• The Boolean symbol is " ”, my spouse and i. e. Q = AB

ITP3902 Discrete Mathematics & Statistics

Page 4

Address 2 Boolean Functions

Common sense gates: CERTAINLY NOT gates

•• A

NOT gate or perhaps an inverter has just one input and produce a great output in line with the following real truth table.

Input

Output

A

0

one particular

1

zero

• The electronic signal symbol is

• The Boolean sign is a pub over the sign, i. elizabeth. Q =

ITP3902 Under the radar Mathematics & Statistics

Web page 5

Lecture 2 Boolean Functions

Boolean Algebra and Functions

• The AND, OR but not functions constitute a complete set to

define a two highly valued Boolean Algebraic system.

• A binary variable is one that can easily take the ideals 0 or 1 . • A Boolean function is definitely an expression formed by binary

variables, the binary operations OR, AND and NOT probably

with parentheses and an equal sign. For any given ideals of

the binary changing, the function can only become either zero or 1 .

ITP3902 Discrete Mathematics & Statistics

Web page 6

Address 2 Boolean Functions

Boolean Algebra Real estate

• The following are some basic properties of Boolean algebra. Personality laws

A+0=A

Aв€™1=A

Idempotent laws

A+A=A

Aв€™ A=A

Inverse laws

A+ =1

Aв€™

Dominance, superiority laws

A+1=1

Aв€™0=0

Commutative laws

A+B=B+A

Aв€™B=Bв€™A

Associative laws

A+(B+C)=(A+B)+C

Aв€™ (Bв€™C)=(Aв€™B)в€™C

Distributive regulations

A & ( B в€™ C ) = ( A + B ) в€™ (A &

C)

Aв€™(B+C)=(Aв€™B)+(Aв€™

C)

Ingestion laws

A+(Aв€™ B)=A

Aв€™ (A+B)=A

Complementation laws

Sobre Morgan's rules

ITP3902 Under the radar Mathematics & Statistics

Site 7

Address 2 Boolean Functions

Real truth Table

Case 1

Employ truth stand to verify the distributive law

Aв€™(B+C)=(Aв€™B)+(Aв€™C)

A

0

0

0

0

1

1

one particular

1

N

0

zero

1

one particular

0

zero

1

you

C

0

1

0

1

zero

1

zero

1

ITP3902 Discrete Mathematics & Figures

B+C

zero

1

1

1

zero

1

one particular

1

Aв€™(B+C)

0

zero

0

0

0

1

1

you

Aв€™B

zero

0

0

0

0

0

one particular

1

Aв€™C

0

zero

0

zero

0

1

0

one particular

(Aв€™B)+

(Aв€™C)

0

zero

0

zero

0

1

1

one particular

Page 8

Lecture 2 Boolean Functions

Truth Desk

2

•Example

Use fact table to exhibit the functional values of f several input principles of back button, y and z.

0

0

0

0

you

1

1

1

zero

0

one particular

1

0

0

you

1

0

1

zero

1

0

1

0

1

ITP3902 Discrete Mathematics & Figures

1

1

1

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