ELECTRICAL ENGINEERING
DIGITAL LOGIC TUTORIAL AND DESIGN
1
DIGITAL LOGIC LAB
(A MINI-LAB EXPERIENCE)
 We are going to build both a combination lock and a
flashing railroad crossing signal using digital logic devices
 To build these circuits we will draw upon knowledge or
resources developed by several areas of electrical
engineering
 First, we will need to learn a little about digital logic
 The worksheet “Explore Logic” in the Excel workbook
entitled, “Lec9-DigitalLab.xls” may be used to verify
your understanding of the next few slides
2
SOME DEFINITIONS
 Definition: Discrete System - a system with a finite number of
sizes or measures
 Shoes, Dresses, Pants, Bolts, Pencils
 Definition: Digital System - a Discrete System with only two
values of system variables: 1 and 0
 True/False; Yes/No; Male/Female; On/Off
 Let’s compare digital and continuous (analog) systems
 Digital signals are binary; analog signals are real-valued numbers
 Digital is less susceptible to noise
3
Analog Waveform
Voltage (V)
5
Time
0
Digital Waveform
1
1
Voltage (V)
5
0
0
Time
4
AND OPERATOR
 Let’s look at the relationship between the semantic and
logical operator known as the AND operator
 Consider:
If the car is fueled AND the engine works,
then the engine will start
 AND means that both conditions
must be true in order for the
conclusion to be true
AND Operator
Truth Table
A B Output
0 0 0
0 1 0
1 0 0
1 1 1
5
DIGITAL AND
 We can build an electrical device that performs the logical AND
operation on voltage equivalents of logic values
 An AND gate has the
electrical schematic:
A
Inputs
B
Output
For digital logic:
True = 1 is 5 volts
False = 0 is 0 volts
• We will practice with the Excel spreadsheet
6
OR OPERATOR
 Another basic operator is the OR
 Consider:
If I have cash OR a credit card,
then I can pay the bill
 OR works such that the output is true, if
either of the two inputs is true
OR Operator
Truth Table
A B Output
0 0 0
0 1 1
1 0 1
1 1 1
7
NOT OPERATOR/INVERTER GATE
 The NOT gate reverses the input
A
B
NOT Operator
Truth Table
 All digital computers are
built using only three gate
types: AND, OR, and NOT
A B
0 1
1 0
8
XOR (EXCLUSIVE OR) OPERATOR
 Let’s look at the relationship between the semantic and
logical operator known as the XOR operator
 Consider a biological example:
If gender A XOR gender B,
then reproduction is possible
 XOR works such that output is activated (equal to one) if
both inputs are of a different value
 Try the Excel spreadsheet exercise
9
DIGITAL XOR
 We can build an electrical device that performs the logical XOR
operation on voltage equivalents of logic values
 An XOR gate has the
electrical schematic:
A
Inputs
B
XOR Operator
Truth Table
Output
A B Output
0 0 0
0 1 1
1 0 1
1 1 0
10
DIGITAL COMBINATION LOCK
DESIGN AND SOFTWARE
SIMULATION
11
MULTI-INPUT AND GATE
 AND gates can be built with any number of inputs
 Consider the symbol for the 4-input AND gate
A
B
C
D
F
 F is true only when all the inputs are true (1’s: ones )
 Using the Excel workbook “Lec9-DigitalLab”, open the
“Digital Locks” worksheet, and test this circuit
12
DIGITAL COMBINATION LOCK
 Using 3 two-input AND gates, we could build a combination
lock that requires a four-digit code, specifically: 1 1 1 1
1
AND
1
1
AND
1
1
AND
1
1
 The number of inputs could be increased by using more and
more AND gates
13
DIGITAL COMBINATION LOCK
 We could build a combination lock that only uses the AND gate, but that would be
of little use since everyone would know our combination, namely 1 1 1 1
 To build a more interesting combination lock, we will utilize the NOT (inverter) gate
0
1
14
DIGITAL COMBINATION LOCK
 Let’s build a combination lock whose input (key code)
combination is 0 1 1 0
0
1
AND
1
1
AND
1
1
AND
0
1
1
 Is there any other combination that works?
15
“PICKING” A DIGITAL LOCK
 Use the truth table to record the
lock outputs for the different lock
combinations in the “Pick the
Locks” worksheet homework
assignment.
Input
Combination
A B C D
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Lock #1
Lock Output
Lock #2 Lock #3 Lock #4
Lock #5
16
DIGITAL RAILROAD CROSSING SIGNAL
DESIGN AND SOFTWARE
SIMULATION
17
DIGITAL RAILROAD CROSSING
SIGNAL
 Now, let’s develop a digital circuit whose output changes over time
 We are all familiar with a railroad crossing signal that alternates flashing red lights
 In addition to constructing the digital combination lock, so let’s begin by designing the
circuit
18
RAILROAD CROSSING SIGNAL
DESIGN
 Here we will need some type of timing signal that will tell the lights when to turn on
and off
 The problem is that we seemingly need two timing signals since one light is on while
the other is off, and vice versa
 A digital logic implementation can allow us to save cost by using only a single timing
signal
 The design effort is then one of considering which gate(s) need to be used to achieve
the alternating signal patterns
19
RAILROAD CROSSING SIGNAL
Turn-on voltage puts
out a constant +5 volts
1 AND 0 outputs 0
1 AND 1 outputs 1
0/1
1
AND
Square wave is
being repeatedly
turned on then off
0/1
XOR
1/0
1 XOR 0 outputs 1
1 XOR 1 outputs 0
20
RAILROAD CROSSING SIGNAL
SIMULATION
 The “Railroad Xing Simulation” worksheet may be used in Excel to view (over
time) the activation of the RR crossing lights
 Note that this Excel simulation uses some advanced features of Excel such as
iteration and conditional formatting to achieve the software simulation
21
ADDITIONAL READING
 How to do Boolean Logic work.
 http://computer.howstuffworks.com/boolean.htm