Download Lecture 14 - Transitors, Gates, and Logic Circuits

Computer Science 101
Logic Circuits
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 High (+5v or 1)
Makes connection
• Base Low (0v or 0)
Disconnects
Base
Switch
Emitter
AND Gate
+5v
• 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
Input
• Input High (+5v or 1)
+5v
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
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: _ ____
AB+(A+B)B
Input Lines for Variables
A
B
Logic Circuit: _ ____
AB+(A+B)B
NOT Gate for B
A
B
_
B
Logic Circuit: _ ____
AB+(A+B)B
_
Subexpression AB
_
AB
A
B
_
B
Logic Circuit: _ ____
AB+(A+B)B
Subexpression A+B
_
AB
A
A+B
B
_
B
Logic Circuit: _ ____
AB+(A+B)B
___
Subexpression A+B
_
AB
A
A+B
B
_
B
____
A+B
Logic Circuit: _ ____
AB+(A+B)B
___
Subexpression (A+B)B
_
AB
A
A+B
B
_
B
____
A+B
____
(A+B)B
Logic Circuit: _ ____
AB+(A+B)B
Entire Expression
_
AB
A
A+B
B
_
B
____
A+B
____
(A+B)B
Logic Circuit  Boolean Exp
• In the opposite direction, given a logic
circuit, we can write a Boolean expression
for the circuit.
• First we label each input line as a variable.
• Then we move from the inputs to label the
outputs from the gates.
• As soon as the input lines to a gate are
labeled, we can label the output line.
• The label on the circuit output is the result.
The Boolean Triangle
Boolean
Expression
Logic
Circuit
Truth
Table