Electrical Engineering 1 WISE Investments Electrical Engineering Lab Digital Logic Tutorial and Design Dr. Keith Holbert

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


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


0

5 Analog Waveform

Time

Vol

tage

(V

)

0

5Digital Waveform

Time

Vol

tage

(V

)

1

0

1


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


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


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


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


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


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


Digital Combination Lock

Design and Software Simulation


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



• 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



• 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



• 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


“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


Digital Railroad Crossing Signal

Design and Software Simulation


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


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


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


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

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Electrical Engineering 1 WISE Investments Electrical Engineering Lab Digital Logic Tutorial and Design Dr. Keith Holbert