Have students work out examples
on their calculators
Physical Logic Gates
Show examples - pass around
7400 ICs
Show overhead of connections
and contents
Emphasize that inputs are voltages,
not currents
Show that the gates are powered,
not passive
One IC contains 4 gates
More details next time
Digital Values
True/False
+5V/0V = GND
On/Off
0/1
High/Low
Logic Gates
Buffer
Tradiational Symbol
IEEE Symbol
Truth Table
Boolean Expression: F = A
Will discuss reason later
Inverters
Traditional Symbol, bubbles
IEEE Symbols: 4 of them, two
types of bubbles
Truth table
Expression: F = bar(A)
Bubble Cancellation
OR
Traditional Symbols
IEEE Symbols
Truth table
Expression: F = A + B = (A'
B')'
AND
Traditional Symbols
IEEE Symbols
Truth table
Expression, F = A B = (A' +
B')'
NAND
Traditional Symbols
IEEE Symbols
Truth table
Expression, F = (A B)' = A'
+ B'
Can make into an inverter by
tying the inputs together
NOR
Traditional Symbols
IEEE Symbols
Truth table
Expression, F = (A + B)' = A'
B'
Can make into an inverter by
tying the inputs together
XOR
Traditional Symbol
IEEE Symbol
Truth table
Expression, F = A (circled +)
B = A B' + A' B
XNOR
Traditional Symbols
IEEE Symbols
Truth table
Expression, F = A (circled .)
B = A B + A' B'
Truth Tables
X is sometimes used in addition
to 0 and 1 to denote "don't care"
Example: Consider a 5 input
AND gate
Old style would require 2^5
rows, all but one of which would be 0
Using X you can show the truth
table with 6 rows
Example: 5 input OR gate
Same points apply
Design Examples
Red Hat Room Illumination
System
Goal: For a room with two entryways,
design a system that will turn on the lights when someone enters
the room. The off switch is manual.
Inputs: A/B = 1 if entering
door A/B is open, 0 otherwise.
Output: L = 1 turns on the lights,
0 leaves the lights in their current state.
Truth table design
Boolean Expression, L = A +
B
Logic Diagrams
Later this quarter will talk
about how to use a counter to turn off the lights as well.
Trimet KFC Alarm
Story: Trimet recently installed
seat sensors that make the drivers uncomfortable and that sounds
an alarm if the driver leaves the seat without setting the handbrake.
This was created to prevent busses from rolling into Kuntucky
Fried Chicken restaurants.
Goal: Design a system that will
sound an alarm if the driver forgets to set the parking brake
before leaving his/her seat.
Inputs: B = 1 if brake is set,
0 if not set; S = 1 if driver is seated, 0 otherwise.
Output: A = 1 to sound the alarm,
0 to keep the alarm off
Truth table
Boolean Expression: A = B' S'
= (A + B)'
Circuit
Show what the circuit would
look like if only had NAND gates
Smart Thermostat
Story: Reduce heating bills
by only turning on the heater when the windows are closed and
the room terperature is less than the set point.
Inputs: W1/W2 = 1 if window
W1/W2 is closed, 0 if open; C = 1 if ambient temp is less than
set point (i.e. it's cold), 0 otherwise.
Output: F = 1 turn on the furnace,
0 turn off the furnace
Truth Table
Equation, F = W1 W2 C
Circuit
Note: 3 variables, unlike the
two previous examples
Barista Quality Assurance
Story: Modify espresso machines
so that they annoy the Barista if he/she tries to make an espresso
with old grounds
Inputs: B = 1 if start button
is down, 0 otherwise; G = 0 if grounds are old, 1 otherwise.
Outputs: A = 1 sound alarm,
0 alarm off; S = 1 turn on steam, 0 otherwise.
Truth table
Expressions, A = B G', S = B
G
Circuit
Note this circuite has two outputs,
unlike the previous examples
Diodes
Diodes only allow current to
flow in one direction
If the voltage across a diode
is greater than about 0.6 V, than it can be modeled as a voltage
source.
If the voltage across the diode
is reversed, almost no current will flow and we can model it
as an open circuit
Show examples with a circuit
that contains a voltage source, resistor, and diode for the diode
pointed both ways.
Show that the actual behavior
is more complicated.
Plot how the actual current
varys as a function of voltage
Plot what our model looks like.
LED's are also diodes, but the
threshold voltage is typically higher, approximately 1.1V.
Pass around samples
Transistors
Draw four types of transistors
BJT NPN (NPN = not pointing
in)
BJT PNP
PMOS
NMOS
Explain that transistors are
three terminal devices that act like a voltage controlled switch
Draw an BJT NPN inverter circuit
Draw a voltage truth table for
Vi = 5V and Vi = 0V
Draw the equivalent circuits
for the input and output in each case
Draw an NMOS,PMOS inverter circuit
Draw a voltage truth table for
Vi = 5V and Vi = 0V
Draw the equivalent circuits
for both cases
You will not be tested on transistors
The goal is to give you an idea
of what they do
Will see transistors in circuit
diagrams for logic gates, but you do not have to understand these
diagrams for this class
Will study these gates in more
detail in other upper division classes
For this class you need to be
able to find the electrical charactersitics and operating conditions
of logic gates from data sheets (discussed next class).