1. A key element of electrical engineering
Digital Circuits
A key element of electrical engineering
sources:

2. Foundations of Electrical Engineering
Electrophysics
Maxwell's Equations, Circuit theory
Information (Communications) Theory
Data rate vs Signal Strength, Error correction
Digital Logic
Using Logic Gates to build up complex ccts 2

3. EE Subdisciplines Power Systems Electromagnetics Solid State
Communication/Signal Processing
Controls
Analog/Digital Design 3

4. What is Voltage? V = “Electrical pressure” - measured in volts.
H2O
High Pressure
Low Pressure
Figure 1.1

5. A battery in an electrical circuit plays the same role as a pump in a water system.

6. 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)

7. Digital Logic is based on Binary
Two possible states
True/False
1/0
Yes/No
On/Off
Light/Dark

8. 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 "0" and CLOSED for "1".
(And there are more ways!)

9. 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.

10. Think Binary! Examples: Logic signal, A, takes on values of
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.

11. Operations on Logic Circuits
Suppose there are 2 logic signals. A and B
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)
OR GATE

12. 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

13. Truth Tables and Logic Gates
Truth tables use 1/0 instead of True/False
OR AND NOT (inverter)

14. NAND GATE = NOT AND A B C A B C An AND gate
followed by NOT
Truth Table Usually drawn as: A
B C A
B C
Any logic gate can be built from 1 or more NAND gates!

16. Lab: LS7400 Quad Nand Gate IC
Pinout shows which pins are connected to what
Vcc = +5 V, -Vcc = 0V
Verify the notch location!!

17. Breadboard a NAND gate
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.

18. Connect Power Supply to Breadboard
Ground +5V
Black to Ground Red to +5V

19. Add signal wires for A and B

20. 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')

21. Move brown wire to change B to '0'
Add LED to output pin 3

22. Are these showing the NAND truth table?

23. How about these?

24. A NAND Inverter A C Connecting the two inputs A and B are both at A
Truth table is the same as Inverter
A C

25. NAND + NAND = AND A B C Taking NOT-NOT AND
Try it! Add wires from Pin 3 to 4, 4 to 5
move your output Resistor to pin 6

26. 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

27. Flip Flop Wiring
And each labelled pin A,B,P,Q have resistors and LED to ground for monitoring

28. Flip Flop in Action
A=0 B=1
A=0 B=0

29. Flip Flop in Action
A=0 B=1  A=1, B=1
A=1 B=0  A=1, B=1

30. 3 NANDs make an OR A C B
Use the digital circuit simulator to try out:

31. 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.

32. 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 "adder" with two outputs: the one-digit result of the add, and the value of a "carry" bit. In binary arithmetic, 1+1=0 with a carry=1.

33. 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 "three toilet" system.
Devise a logic circuit whose "1" inputs represent "flushes"
and whose "1" 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.