# Digital Circuits ```Digital Circuits
A key element of electrical engineering
sources:
http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/EEIndex.html
http://www.jhu.edu/~virtlab/logic/log_cir.htm
Foundations of Electrical
Engineering

Electrophysics
 Maxwell's

Information (Communications) Theory
 Data

Equations, Circuit theory
rate vs Signal Strength, Error correction
Digital Logic
 Using
Logic Gates to build up complex ccts
2
Lecture 1
EE Subdisciplines
Power Systems
 Electromagnetics
 Solid State
 Communication/Signal Processing
 Controls
 Analog/Digital Design

3
Lecture 1
What is Voltage?
V = “Electrical pressure”
- measured in volts.
H2O
High Pressure
Low Pressure
Figure 1.1
4
A battery in an electrical circuit plays the same
role as a pump in a water system.
5
Where can I find a digital circuit?
• Digital Circuits and Digital Logic are the buiding
blocks for
– computers
– certain control systems (robots, factories)
– LED displays
• Digital Circuits are built up from Analog circuits
– analog: continuous varying, digital: discrete steps
– electricity has many characteristics of logic
(+/-, True/False, etc)
Digital Logic is based on Binary
• Two possible states
– True/False
– 1/0
– Yes/No
– On/Off
– Light/Dark
Logic Signals
• Different systems for representing binary info in
the physical world:
– A voltage signal:
• Zero (0) corresponding to 0 volts
• One (1) corresponding to five volts.
– A sinewave:
• Zero corresponding to some frequency
• One corresponding to some other frequency.
– Switches:
• OPEN for &quot;0&quot; and CLOSED for &quot;1&quot;.
– (And there are more ways!)
Characteristics of Logic Signals
• Change in time
– Initially we look at unchanging values
• Voltage signal takes on two values
– corresponding to 0 and 1.
– for example, 0 Volts and 5 volts
• We can associate a variable with a logic signal
– assign a symbol to represent that variable
– like the symbol A.
Think Binary!
• Examples:
– Cell phone converts voice into series of ones and zeros
– Thermostat: 1 when temp is too low, 0 when too high
• Logic signal, A, takes on values of
0 (FALSE, OFF) or 1 (TRUE, ON).
– might be a voltage, a switch closure, etc.
– More generally, think in terms of zeros and ones
• not in terms of the values of the voltage or switches.
Operations on Logic Circuits
• Suppose there are 2 logic signals. A and B
OR GATE
• We often want to derive a 3rd signal C based on
the values of A and B
– if it is dark outside (A) OR raining (B)
• Turn on lights (C)
Logic Gates
• Logic Gates are digital circuit packages that
perform logic operations on logic signals
– AND gate: both must be true for true output
– OR gate: only one must be true for true output
– NOT gate: true in means false out and vice versa
– NAND gate: the opposite of AND
• AND followed by NOT
Truth Tables and Logic Gates
• Truth tables use 1/0 instead of True/False
• OR
AND
NOT (inverter)
NAND GATE = NOT AND
• An AND gate
– followed by NOT
A
B
• Truth Table
•
•
C
Usually drawn as:
A
B
Any logic gate can be built
from 1 or more NAND gates!
C
Lab: LS7400 Quad Nand Gate IC
• Pinout shows which pins are
connected to what
• Vcc = +5 V, -Vcc = 0V
• Verify the notch location!!
• a breadboard is a quick way to build circuits
without soldering
• 5 pin rows are connected by metal clips
• vertical column
on sides are
connected.
Black to Ground
Red to +5V
Ground
+5V
for A and B
Add LEDs to show value of A,B
(1- 470 Ohm Resistor for each LED)
The shorter Wire on LED goes to
GROUND
When both are connected,
turn on power (A, B are '1')
Move brown wire to change B to '0'
Add LED to output pin 3
Are these showing
the NAND truth table?
A NAND Inverter
• Connecting the two inputs
A
– A and B are both at A
– Truth table is the same as Inverter
C
NAND + NAND = AND
• Taking NOT-NOT AND
A
B
Try it! Add wires from Pin 3 to 4, 4 to 5
move your output Resistor to pin 6
C
FLIP FLOP – another 2 NAND cct
• Output of 1 (P)
– feeds back to input of 2
• Output of 2 (Q)
– feeds back to input of 1
MEMORY!!
previous state was X=1, Y=0
previous state was X=0, Y=1
Flip Flop Wiring
And each labelled pin A,B,P,Q have resistors
and LED to ground for monitoring
Flip Flop in Action
A=0 B=0
A=0 B=1
Flip Flop in Action
A=0 B=1  A=1, B=1
A=1 B=0  A=1, B=1
3 NANDs make an OR
A
C
B
Use the digital circuit simulator to try out:
http://www.jhu.edu/~virtlab/logic/logic.htm
Team Challenges (simulate or wire up)
Using only NAND gates:
A . Design, construct and test a three input AND.
B. Design, construct and test a three input NAND.
C. Design a four input NAND.
Hint: If wiring, use an LED indicator to show the
inputs and/or the outputs in your circuits.
Use a current-limiting resistor for each LED.
Use the circuit builder
http://www.jhu.edu/~virtlab/logic/logic.htm
D. Using only AND, NOT, and OR produce a
three-input OR circuit, ie., the output is 1 if
any of the inputs is 1.
E. Create a two-input &quot;adder&quot; with two outputs:
the one-digit result of the add, and the value
of a &quot;carry&quot; bit. In binary arithmetic, 1+1=0
with a carry=1.
Super Bowl Problem
• At the beginning of halftime during the Superbowl,
– 35 million toilets are flushed almost simultaneously.
– Resulting loss of water pressure wreaks havoc on many
municipal water systems.
• Make a controller to solve the problem for a &quot;three toilet&quot;
system.
– Devise a logic circuit whose &quot;1&quot; inputs represent &quot;flushes&quot;
– and whose &quot;1&quot; outputs represent opened water valves
– If no more than one toilet is flushed, then that toilet's water
valve opens,
• the others remaining closed.
– If more than one toilet is flushed, then all the water valves
remain closed.
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