Lecture two Boolean Capabilities

Lecture 2

Basic Boolean functions, reasoning gates and

Karnaugh maps

ITP3902 Under the radar Mathematics & Statistics

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Address 2 Boolean Functions

Logic gates

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

вЂў Open or close;

вЂў Hollywood or low voltage

вЂў A certain sign is present or absent, etc .

вЂў Both possible says are called 1 or 0.

вЂў 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).

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

ITP3902 Discrete Mathematics & Statistics

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Address 2 Boolean Functions

Logic gates: OR PERHAPS gates

вЂў 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

вЂў The digital circuit symbol is

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

ITP3902 Discrete Math & Stats

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Lecture 2 Boolean Capabilities

Logic entrances: AND entrance

вЂў 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

вЂў The electronic circuit symbol is definitely

вЂў The Boolean symbol is " пѓ—вЂќ, my spouse and i. e. Q = Aпѓ—B

ITP3902 Discrete Mathematics & Statistics

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Address 2 Boolean Functions

Common sense gates: CERTAINLY NOT gates

вЂўвЂў 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

вЂў The electronic signal symbol is

вЂў 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

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

define a two highly valued Boolean Algebraic system.

вЂў A binary variable is one that can easily take the ideals 0 or 1 . вЂў 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

вЂў 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

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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

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Lecture 2 Boolean Functions

Truth Desk

2

вЂўExample

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