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

2. Electrical Engineering 2 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

3. Electrical Engineering 3 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

4. Electrical Engineering 4 0 5 Analog Waveform Time Voltage (V) 0 5 Digital Waveform Time Voltage (V) 1 0 1

5. Electrical Engineering 5 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 000 ABOutput 010 100 111 AND means that both conditions must be true in order for the conclusion to be true

6. Electrical Engineering 6 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 volts False = 0 is 0 volts A Inputs B Output Practice with the Excel spreadsheet

7. Electrical Engineering 7 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 000 ABOutput 011 101 111 OR Operator Truth Table

8. Electrical Engineering 8 NOT Operator/Inverter Gate The NOT gate reverses the input NOT Operator Truth Table All digital computers are built using only three gate types: AND, OR, and NOT 01 AB 10 AB

9. Electrical Engineering 9 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

10. Electrical Engineering 10 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 Operator Truth Table 000 ABOutput 011 101 110 A Inputs Output B

11. Electrical Engineering 11 Digital Combination Lock Design and Software Simulation

12. Electrical Engineering 12 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 ABCDABCD F

13. Electrical Engineering 13 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 1 1 1 1 1 1 1

14. Electrical Engineering 14 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 01

15. Electrical Engineering 15 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 1 1 1 1 1 1 1 0 0

16. Electrical Engineering 16 “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

17. Electrical Engineering 17 Digital Railroad Crossing Signal Design and Software Simulation

18. Electrical Engineering 18 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

19. Electrical Engineering 19 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

20. Electrical Engineering 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

21. Electrical Engineering 21 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