01_05 Logic Gates

Logic Gates

Introduction to Digital Logic Basics Hardware consists of a few simple building blocks ¤ These are called logic gates ۞AND, OR, NOT, … ۞NAND, NOR, XOR, …

Logic gates are built using transistors ۞NOT

gate can be implemented by a single transistor ۞AND gate requires 3 transistors

Transistors are the fundamental devices ۞Pentium

consists of 3 million transistors ۞Compaq Alpha consists of 9 million transistors ۞Now we can build chips with more than 100 million transistors

AND Gate AND X Z Y Z = X & Y

X 0 0 1 1

Y 0 1 0 1

Z 0 0 0 1

OR Gate OR X Y Z = X | Y

Z

X 0 0 1 1

Y 0 1 0 1

Z 0 1 1 1

NOT Gate -- Inverter NOT X

Y Y = ~X

X

Y

0 1

1 0

NAND Gate NAND X Z Y Z = ~(X & Y) nand(Z,X,Y)

X 0 0 1 1

Y 0 1 0 1

Z 1 1 1 0

NAND Gate NOT-AND X W Y W = X & Y Z = ~W = ~(X & Y)

Z

X 0 0 1 1

Y 0 1 0 1

W 0 0 0 1

Z 1 1 1 0

NOR Gate NOR X Y

Z = ~(X | Y) nor(Z,X,Y)

Z

X 0 0 1 1

Y 0 1 0 1

Z 1 0 0 0

NOR Gate NOT-OR X

W

Y W = X | Y Z = ~W = ~(X | Y)

Z

X 0 0 1 1

Y 0 1 0 1

W 0 1 1 1

Z 1 0 0 0

Proving NAND gate is universal

Proving NOR gate is universal

Conclusion:: Any circuit which is designed by using NOT, AND, and OR gates can also be designed using only NAND gates.

Any circuit which is designed by using NOT, AND, and OR gates can also be designed using only NOR gates.

14

Exclusive-OR Gate XOR X Y

Z

X  Y  XY  XY

X Y

Z

0 0 1 1

0 1 1 0

0 1 0 1

Exclusive-NOR Gate XNOR X Y

Z XY

Z

X Y

Z

0 0 1 1

1 0 0 1

0 1 0 1

Logical Gates and Combinatorial Circuits In circuitry theory, NOT, AND, and OR gates are the basic gates. Any circuit can be designed using these gates. The circuits designed depend only on the inputs, not on the output. In other words, these circuits have no memory. Also these circuits are called combinatorial circuits. The symbols NOT gate, AND gate, and OR gate are also considered as basic circuit symbols, which are used to build general circuits.

Summary Summary for all 2-input gates Inputs

Output of each gate

A

B

AND

NAND

OR

NOR

XOR

XNOR

0

0

0

1

0

1

0

1

0

1

0

1

1

0

1

0

1

0

0

1

1

0

1

0

1

1

1

0

1

0

0

1

THE

END