Electrical Engineering 1 WISE Investments Electrical Engineering Lab Digital Logic Tutorial and...

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

Electrical Engineering4

0

5 Analog Waveform

Time

Vol

tage

(V

)

0

5Digital Waveform

Time

Vol

tage

(V

)

1

0

1

Electrical Engineering5

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

Electrical Engineering12

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

Electrical Engineering15

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

Electrical Engineering16

“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

Electrical Engineering21

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