introduction to computer engineering by richard e. haskell basic logic gates module m1.1 section 3.1
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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
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
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
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
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