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

4 0 5 Analog Waveform Time Voltage (V) 0 5 Digital Waveform Time Voltage (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 start  AND means that both conditions must be true in order for the conclusion to be true 5 AND Operator Truth Table 000 ABOutput

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: 6 For digital logic: True = 1 is 5 volts False = 0 is 0 volts A Inputs B Output We will 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 ABOutput OR Operator Truth Table

NOT OPERATOR/INVERTER GATE  The NOT gate reverses the input  All digital computers are built using only three gate types: AND, OR, and NOT 8 NOT Operator Truth Table 01 AB 10 AB

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: 10 XOR Operator Truth Table 000 ABOutput A Inputs Output B

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  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 ABCDABCD F

DIGITAL COMBINATION LOCK  Using 3 two-input AND gates, we could build a combination lock that requires a four-digit code, specifically:  The number of inputs could be increased by using more and more AND gates 13 AND

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  To build a more interesting combination lock, we will utilize the NOT (inverter) gate 14 01

DIGITAL COMBINATION LOCK  Let’s build a combination lock whose input (key code) combination is  Is there any other combination that works? 15 AND

“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. 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

20 RAILROAD CROSSING SIGNAL Turn-on voltage puts out a constant +5 volts Square wave is being repeatedly turned on then off AND 0/1 1 1/0 1 AND 0 outputs 0 1 AND 1 outputs 1 1 XOR 0 outputs 1 1 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 21

ADDITIONAL READING  How to do Boolean Logic work. 