WISE Investments Electrical Engineering Lab Digital Logic Tutorial

WISE Investments Electrical Engineering Lab Digital Logic Tutorial and Design Dr. Keith Holbert Electrical Engineering 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, “EE-WISE-Digital. Lab. xls” may be used to verify your understanding of the next few slides Electrical Engineering 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 Electrical Engineering 3

Analog Waveform Voltage (V) 5 Time 0 Digital Waveform 1 1 Voltage (V) 5 0 Time 0 Electrical Engineering 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 Operator Truth Table • AND means that both conditions A B Output must be true in order for the 0 0 0 conclusion to be true 0 1 0 0 1 1 1 Electrical Engineering 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 Output B For digital logic: True = 1 is 5 volts False = 0 is 0 volts • Practice with the Excel spreadsheet Electrical Engineering 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 Electrical Engineering OR Operator Truth Table A B Output 0 0 1 1 1 0 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 Electrical Engineering 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 Electrical Engineering 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 Electrical Engineering Output XOR Operator Truth Table A B Output 0 0 1 1 1 0 10

Digital Combination Lock Design and Software Simulation Electrical Engineering 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) • Using the Excel workbook “EE-WISE-Digital. Lab”, open the “Digital Locks” worksheet, and test this circuit Electrical Engineering 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 AND 1 1 1 • The number of inputs could be increased by using more and more AND gates Electrical Engineering 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 • To build a more interesting combination lock, we will utilize the NOT (inverter) gate 0 Electrical Engineering 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 0 1 1 • Is there any other combination that works? Electrical Engineering 15

“Picking” a Digital Lock • Use the truth table below to record the lock outputs for the different lock combinations in the “Pick the Locks” worksheet Electrical Engineering 16

Digital Railroad Crossing Signal Design and Software Simulation Electrical Engineering 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, we will build the railroad crossing signal in the lab, so let’s begin by designing the circuit Electrical Engineering 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 Electrical Engineering 19

Railroad Crossing Signal Turn-on voltage puts out a constant +5 volts 1 Square wave is being repeatedly turned on then off 0/1 1 AND 0 outputs 0 1 AND 1 outputs 1 AND XOR 0/1 1/0 1 XOR 0 outputs 1 1 XOR 1 outputs 0 Electrical Engineering 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 Electrical Engineering 21