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1Electrical Engineering
WISE InvestmentsElectrical Engineering Lab
Digital Logic Tutorial and Design
Dr. Keith Holbert
Electrical Engineering2
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, “EE-WISE-DigitalLab.xls” may be used to verify your understanding of the next few slides
Electrical Engineering3
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
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0
5 Analog Waveform
Time
Vol
tage
(V
)
0
5Digital Waveform
Time
Vol
tage
(V
)
1
0
1
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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 startAND Operator
Truth Table
0 0 0A B Output
0 1 01 0 01 1 1
• AND means that both conditions must be true in order for the conclusion to be true
Electrical Engineering6
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:
For digital logic:
True = 1 is 5 voltsFalse = 0 is 0 volts
AInputs
B
Output
• Practice with the Excel spreadsheet
Electrical Engineering7
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
0 0 0A B Output
0 1 11 0 11 1 1
OR OperatorTruth Table
Electrical Engineering8
NOT Operator/Inverter Gate
• The NOT gate reverses the input
NOT OperatorTruth Table
• All digital computers are built using only three gate types: AND, OR, and NOT
0 1A B
1 0
A B
Electrical Engineering9
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
Electrical Engineering10
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:
XOR OperatorTruth Table
0 0 0A B Output
0 1 11 0 11 1 0
A
InputsOutput
B
11Electrical Engineering
Digital Combination Lock
Design and Software Simulation
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Multi-Input AND Gate
• AND gates can be built with any number of inputs
• Consider the symbol for the 4-input AND gate
• F is true only when all the inputs are true (1’s)
• Using the Excel workbook “EE-WISE-DigitalLab”, open the “Digital Locks” worksheet, and test this circuit
ABCD
F
Electrical Engineering13
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
• The number of inputs could be increased by using more and more AND gates
AND
AND
AND 1
1
1
1
1
1
1
Electrical Engineering14
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
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Digital Combination Lock
• Let’s build a combination lock whose input (key code) combination is 0 1 1 0
• Is there any other combination that works?
AND
AND
AND
1
1
1
1
1
1
1
0
0
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“Picking” a Digital Lock• Use the truth table below to record the lock outputs for the
different lock combinations in the “Pick the Locks” worksheetInput
Combination Lock OutputA B C D Lock #1 Lock #2 Lock #3 Lock #4 Lock #50 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1
17Electrical Engineering
Digital Railroad Crossing Signal
Design and Software Simulation
Electrical Engineering18
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, we will build the railroad crossing signal in the lab, so let’s begin by designing the circuit
Electrical Engineering19
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
Electrical Engineering20
Railroad Crossing Signal
Turn-on voltage puts out a constant +5 volts
Square wave is being repeatedly
turned on then off
AND0/1
1
0/1
1/0
1 AND 0 outputs 01 AND 1 outputs 1
1 XOR 0 outputs 11 XOR 1 outputs 0
XOR
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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