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Basic Logic Gates

- Module M1.1
- Section 3.1

Basic Logic Gates

- NOT, AND, and OR Gates
- NAND and NOR Gates
- DeMorgans Theorem
- Exclusive-OR (XOR) Gate

NOT Gate -- Inverter

Y

X

0 1

1 0

NOT

- Y !X
- Y X
- Y X
- Y X

NOT

X

!X

!!X X

X !X !!X 0 1 0 1 0 1

AND Gate

AND

X Y Z 0 0 0 0 1 0 1 0 0 1 1 1

X

Z

Y

Z X Y

AND

- X Y
- X Y
- X Y
- X Y
- XY

V

U

OR Gate

OR

X Y Z 0 0 0 0 1 1 1 0 1 1 1 1

X

Z

Y

Z X Y

OR

- X Y
- X Y
- X V Y
- X U Y

NAND Gate

NAND

X Y Z 0 0 1 0 1 1 1 0 1 1 1 0

X

Z

Y

Z !(X Y)

NAND Gate

NOT-AND

X Y W Z 0 0 0 1 0 1 0 1 1 0 0 1 1 1

1 0

X

W

Z

Y

W X Y Z !W !(X Y)

NOR Gate

NOR

X Y Z 0 0 1 0 1 0 1 0 0 1 1 0

X

Z

Y

Z !(X Y)

NOR Gate

NOT-OR

X Y W Z 0 0 0 1 0 1 1 0 1 0 1 0 1 1

1 0

X

W

Z

Y

W X Y Z !W !(X Y)

NAND Gate

X

Z

X

Z

Y

Y

Z !(X Y)

Z !X !Y

X Y W Z 0 0 0 1 0 1 0 1 1 0 0 1 1 1

1 0

X Y !X !Y Z 0 0 1 1 1 0 1 1 0 1 1 0 0

1 1 1 1 0 0 0

De Morgans Theorem-1

!(X Y) !X !Y

- NOT all variables
- Change to and to
- NOT the result

NOR Gate

X

X

Z

Z

Y

Y

Z !(X Y)

Z !X !Y

X Y Z 0 0 1 0 1 0 1 0 0 1 1 0

X Y !X !Y Z 0 0 1 1 1 0 1 1 0 0 1 0 0

1 0 1 1 0 0 0

De Morgans Theorem-2

!(X Y) !X !Y

- NOT all variables
- Change to and to
- NOT the result

De Morgans Theorem

- NOT all variables
- Change to and to
- NOT the result
- --------------------------------------------
- !X !Y !(!!X !!Y) !(X Y)
- !(X Y) !!(!X !Y) !X !Y
- !X !Y !(!!X !!Y) !(X Y)
- !(X Y) !!(!X !Y) !X !Y

Exclusive-OR Gate

XOR

X Y Z

Z

X

0 0 0

Y

0 1 1

Z X Y

1 0 1

1 1 0

Exclusive-OR Gate

X Y !X !Y !XY X!Y Z

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

0 1 1 1 1 0 0 0 0 0

Problem

Z

Write the logic equation for Z in terms of X and Y

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