Digital Logic Tutorial and Design electronicsteacher

1. Digital Logic Tutorial and Design http://www.electronicsteacher.com

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

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

5. AND means that both conditions must be true in order for the conclusion to be true 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 A B Output 0 0 0 0 1 0 0 0 1 1 1 1 AND Operator AND Operator Truth Table

6. A Output Inputs B 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 • Practice with the Excel spreadsheet

7. A B Output 0 1 0 0 1 0 1 0 1 1 1 1 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 OR Operator Truth Table

8. The NOT gate reverses the input All digital computers are built using only three gate types: AND, OR, and NOT A B A B 0 1 1 0 NOT Operator/Inverter Gate NOT Operator Truth Table

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. A A B Output Output Inputs 0 1 B 0 0 1 0 1 0 1 1 1 0 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

11. Digital Combination Lock Design and Software Simulation

12. AND gates can be built with any number of inputs Consider the symbol for the 4-input AND gate F is trueonly when all the inputs are true (1’s) Using the Excel workbook “EE-WISE-DigitalLab”, open the “Digital Locks” worksheet, and test this circuit A B C D F Multi-Input AND Gate

13. 1 AND 1 1 AND 1 1 AND 1 1 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

14. 0 1 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

15. Let’s build a combination lock whose input (key code) combination is 0 1 1 0 Is there any other combination that works? Digital Combination Lock 1 0 AND 1 AND 1 1 1 AND 1 0 1

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. Digital Railroad Crossing Signal Design and Software Simulation

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

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