Download - 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
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
