Download A + B

Computer Science 210
Computer Organization
Introduction to
Logic Circuits
(Chapter 3)
From Boolean Logic
to Hardware
• Boolean values true and false map to binary values 1
and 0
• Binary values 1 and 0 map to discrete states on and
off
• Discrete states on and off map to voltage levels +5V
and 0V on an analog device
• Connect these devices to perform logical operations
Transistor - Electronic Switch
Collector
Base
Switch
Emitter
• Base High (+5v or 1)
Makes connection
• Base Low (0v or 0)
Disconnects
AND Gate
+5
v
• Output is 1 only if
– Input-1 is 1 and
– Input-2 is 1
• Output
= Input1 AND Input2
Input-1
AND Gate
A
Input-2
B
Output
AB
OR Gate
• Output is 1 if
– A is 1 or if
– B is 1
+5v
• Output
= A OR B
A
B
OR Gate
A
Output
B
A+B
NOT Gate
+5
v
Input
• Input High (+5v or 1)
Output Low (0v or 0)
Output • Input Low (0v or 0)
Output High (+5v or
1)
• Output is opposite of
Input
NOT Gate
Ground
A
_
A
Basic Gates
AND Gate
NAND Gate
A
A
B
B
AB
OR Gate
NOR Gate
A
A
B
B
A+B
NOT Gate
A
___
AB
_
A
_____
A+B
Boolean Exp  Logic Circuit
• To draw a circuit from a Boolean expression:
– From the left, make an input line for each variable.
– Next, put a NOT gate in for each variable that appears
negated in the expression.
– Still working from left to right, build up circuits for the
subexpressions, from simple to complex.
Logic Circuit
A~B + ~(A+B)B
Input Lines for Variables
A
B
Logic Circuit
A~B + ~(A+B)B
NOT Gate for B
A
B
_
B
Logic Circuit
A~B + ~(A+B)B
_
Subexpression AB
_
AB
A
B
_
B
Logic Circuit
A~B + ~(A+B)B
Subexpression A+B
_
AB
A
A+B
B
_
B
Logic Circuit
A~B + ~(A+B)B
___
Subexpression A+B
_
AB
A
A+B
B
_
B
____
A+B
Logic Circuit
A~B + ~(A+B)B
___
Subexpression (A+B)B
_
AB
A
A+B
B
_
B
____
A+B
____
(A+B)B
Logic Circuit
A~B + ~(A+B)B
Entire Expression
_
AB
A
A+B
B
_
B
____
A+B
____
(A+B)B
The Boolean Triangle
Boolean
Expression
Logic
Circuit
Truth
Table