Introduction to Computer Engineering by Richard E. Haskell

Basic Logic Gates

Module M1.1

Section 3.1

Introduction to Computer Engineering by Richard E. Haskell

Basic Logic Gates

• NOT, AND, and OR Gates

• NAND and NOR Gates

• DeMorgan’s Theorem

• Exclusive-OR (XOR) Gate

Introduction to Computer Engineering by Richard E. Haskell

X Y

Y = !X

NOT

NOT Gate -- Inverter

X Y

01

10

Introduction to Computer Engineering by Richard E. Haskell

NOT

• Y = !X

• Y = X’

• Y = X

• Y = X

Introduction to Computer Engineering by Richard E. Haskell

NOT

X !X !!X = X

X !X !!X0 1 01 0 1

Introduction to Computer Engineering by Richard E. Haskell

AND GateAND

X

Y

Z

Z = X & Y

X Y Z0 0 00 1 01 0 01 1 1

Introduction to Computer Engineering by Richard E. Haskell

AND

• X & Y• X Y• X Y• X * Y• XY

U

V

Introduction to Computer Engineering by Richard E. Haskell

OR Gate

OR

X

YZ

Z = X # Y

X Y Z0 0 00 1 11 0 11 1 1

Introduction to Computer Engineering by Richard E. Haskell

OR

• X # Y• X + Y• X V Y• X U Y

Introduction to Computer Engineering by Richard E. Haskell

NAND GateNAND

X

Y

Z

Z = !(X & Y)

X Y Z0 0 10 1 11 0 11 1 0

Introduction to Computer Engineering by Richard E. Haskell

NAND Gate

NOT-AND

X

Y

Z

W = X & Y

Z = !W = !(X & Y)

X Y W Z0 0 0 10 1 0 11 0 0 11 1 1 0

W

Introduction to Computer Engineering by Richard E. Haskell

NOR Gate

NOR

X

YZ

Z = !(X # Y)

X Y Z0 0 10 1 01 0 01 1 0

Introduction to Computer Engineering by Richard E. Haskell

NOR Gate

NOT-OR

X

Y

W = X # Y

Z = !W = !(X # Y)

X Y W Z0 0 0 10 1 1 01 0 1 01 1 1 0

ZW

Introduction to Computer Engineering by Richard E. Haskell

NAND Gate

X

Y

X

Y

Z Z

Z = !(X & Y) Z = !X # !Y

=

X Y W Z0 0 0 10 1 0 11 0 0 11 1 1 0

X Y !X !Y Z0 0 1 1 10 1 1 0 11 0 0 1 11 1 0 0 0

Introduction to Computer Engineering by Richard E. Haskell

De Morgan’s Theorem-1

!(X & Y) = !X # !Y

• NOT all variables• Change & to # and # to &• NOT the result

Introduction to Computer Engineering by Richard E. Haskell

NOR Gate

X

YZ

Z = !(X # Y)

X Y Z0 0 10 1 01 0 01 1 0

X

YZ

Z = !X & !Y

X Y !X !Y Z0 0 1 1 10 1 1 0 01 0 0 1 01 1 0 0 0

Introduction to Computer Engineering by Richard E. Haskell

De Morgan’s Theorem-2

!(X # Y) = !X & !Y

• NOT all variables• Change & to # and # to &• NOT the result

Introduction to Computer Engineering by Richard E. Haskell

De Morgan’s 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

Introduction to Computer Engineering by Richard E. Haskell

Exclusive-OR Gate

X Y ZXOR

XY

Z

Z = X $ Y

0 0 00 1 11 0 11 1 0

Introduction to Computer Engineering by Richard E. Haskell

X Y

X !X Y !Y

Exclusive-OR Gate

0 0 1 1 0 0 00 1 1 0 1 0 11 0 0 1 0 1 11 1 0 0 0 0 0

X Y !X !Y !X&Y X&!Y Z

Introduction to Computer Engineering by Richard E. Haskell

ProblemX Y

X !X Y !Y

Z

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