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Logic GatesLogic Gates

Benchmark Companies Inc

PO Box 473768

Aurora CO 80047

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AND Function (7408)Output Y is TRUE if inputs A AND B are TRUE, else it is FALSE.

Logic Symbol

Text Description

Truth Table

Boolean Expression

ANDA

BY

INPUTS OUTPUT

A B Y 0 0 0 0 1 0 1 0 0 1 1 1

AND Gate Truth Table

Y = A x B = A • B = AB

AND Symbol

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OR Function (7432)Output Y is TRUE if input A OR B is TRUE, else it is FALSE.

Logic Symbol

Text Description

Truth Table

Boolean Expression Y = A + B

OR Symbol

A

BYOR

INPUTS OUTPUT

A B Y 0 0 0 0 1 1 1 0 1 1 1 1

OR Gate Truth Table

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NOT Function (inverter)(7404)Output Y is TRUE if input A is FALSE, else it is FALSE. Y is the inverse of A.

Logic Symbol

Text Description

Truth Table

Boolean Expression

INPUT OUTPUT

A Y 0 1 1 0

NOT Gate Truth Table

A YNOT

NOT Bar

Y = A Y = A’Alternative Notation

Y = !A

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NAND Function (7400)Output Y is FALSE if inputs A AND B are TRUE, else it is TRUE.

Logic Symbol

Text Description

Truth Table

Boolean Expression

A

BYNAND

A bubble is an inverterThis is an AND Gate with an inverted output

Y = A x B = AB

INPUTS OUTPUT

A B Y 0 0 1 0 1 1 1 0 1 1 1 0 NAND Gate Truth Table

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NOR Function (7402)Output Y is FALSE if input A OR B is TRUE, else it is TRUE.

Logic Symbol

Text Description

Truth Table

Boolean Expression Y = A + B

A

BYNOR

A bubble is an inverter.This is an OR Gate with its output inverted.

INPUTS OUTPUT

A B Y 0 0 1 0 1 0 1 0 0 1 1 0

NOR Gate Truth Table

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Circuit-to-Truth Table Example

OR

A

Y

NOT

AND

B

CAND

2# of Inputs = # of Combinations

2 3 = 8

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y

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Circuit-to-Truth Table Example

OR

A

Y

NOT

AND

B

CAND

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y

00

0

0

1 0

0

0

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y0

OR

A

Y

NOT

AND

B

CAND

00

1

0

1 1

1

1

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y010

OR

A

Y

NOT

AND

B

CAND

01

0

0

1 0

0

0

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y010

0

OR

A

Y

NOT

AND

B

CAND

01

1

0

1 1

1

1

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y0101

0

OR

A

Y

NOT

AND

B

CAND

10

0

0

0 0

0

0

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y01010

0

OR

A

Y

NOT

AND

B

CAND

10

1

0

0 0

0

0

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y010100

0

OR

A

Y

NOT

AND

B

CAND

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0

1

0 0

1

1

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Circuit-to-Truth Table Example

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y0101001

0

OR

A

Y

NOT

AND

B

CAND

11

1

1

0 0

1

1

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Circuit-to-Boolean Equation

OR

A

Y

NOT

ANDB

CAND

A B

A C

A = A B + A C

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

A B C Y

0

0

00

0

11

}

1

1

}

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A - O - I Logic

OR

A

Y

NOT

ANDB

CAND

AND Gates

INVERTER Gates

OR GatesOther Logic Arrangements:

NAND - NAND LogicNOR - NOR Logic

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NAND Gate – Special Application

INPUTS OUTPUT

A B Y 0 0 1 0 1 1 1 0 1 1 1 0

A

BYNAND

TNANDS

S T0010 11 0

Equivalent To An Inverter Gate

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NOR Gate - Special Application

S T0010 11 0

Equivalent To An Inverter Gate

TS NOR

A

BYNOR

INPUTS OUTPUT

A B Y 0 0 1 0 1 0 1 0 0 1 1 0

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End of Presentation