LABORATORY11: Digital Logic Circuits

1. LABORATORY11:Digital Logic Circuits General Engineering Polytechnic University

2. Objectives Logic Functions Sample Problem Truth Table Boolean Equation Karnaugh Maps (K-maps) Simplified Boolean Equation Combinational Logic Circuit Integrated Circuits (ICs) IC Identification Digital Logic Trainer Materials for Lab Problem Statement Procedure Written Assignment Written Topics Recitation Topics Closing Overview

3. Objectives • Understand the functions of logic gates • Become familiar with digital circuits Use you new knowledge to design & implement a combinational logic circuit using the digital trainer

4. Logic Functions • AND - “The all or nothing operator” • Output is high (1) only when ALL inputs are high (1) • OR gate - “The any or all operator” • Output is high (1) when at least ONE input is high (1) • NOT (INVERTER) operator • Output is opposite of input • Only one input and one output

5. Logic Function Logic Symbol Boolean Expression Truth Table Inputs Outputs A Y AND A B Y B A • B = Y 0 0 0 0 0 1 1 0 0 A Y 1 1 1 A + B = Y OR B 0 0 0 0 1 1 1 0 1 1 A Ā 1 1 NOT A = Ā 0 1 1 0 Logic Functions

6. Sample Problem • An ATM machine has three options, Print statement, Withdraw money, or Deposit Money • The ATM machine will charge you $1.00 if you: • Want to withdraw • Only want to print out your statement (no transactions at all)

7. A truth table is a table that displays all possible input combinations and the resulting outputs. INPUT OUTPUT P = print C = charge W = withdraw D = deposit 0 = “do not” 0 = $0.00 1 = “do” 1 = $1.00 INPUTS OUTPUT W D C P 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Truth Table

8. INPUTS OUTPUT W D C P 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Boolean Equation = PWD Outputs with a value of “ONE” are kept C = + PWD + PWD + PWD + PWD

9. Place output ONE in corresponding boxes. Circle neighboring ONES in multiples of 2, try to find the greatest amount of “neighbors” Only overlap circles as a last resort Karnaugh Maps (K-maps) C = PWD+ PWD+ PWD + PWD + PWD PWD PWD PWD 0 0 0 1 1 1 1 0 P W P W P W P W 1 1 1 0 D 1 1 1 D _ Why can’t you switch PW and PW? Why can’t you loop the three adjacent 1s in the top row together?

10. _ _ PWD _ PWD D D _ PWD P W 1 1 _ _ PWD 1 1 P W _ PWD 1 1 1 P W PWD 1 1 1 1 P W Simplified Boolean Equation Opposite values cancel out C = W _ + PD

11. W C = + P D W + P D W + P D D D + P Combinational Logic Circuit W W P _ PD P _ D D

12. Integrated Circuits (ICs) • Used to implement combinational logic circuits • We use the TTL family (transistor transistor logic)

13. 1 14 1 1 14 14 2 13 2 2 13 13 3 12 3 3 12 12 4 11 A 1 V cc 4 4 11 11 Y 1 A 6 5 10 5 5 10 10 A 1 V cc A 2 Y 6 A 1 V cc B 1 B 4 Y 2 A 5 6 9 B 1 B 4 6 6 9 9 Y 1 A 4 A 3 Y 5 Y 1 A 4 A 2 Y 4 7 8 Y 3 A 2 A 4 Y 4 B 2 7 7 8 8 B 3 B 2 B 3 GND Y 4 Y 2 A 3 Y 2 A 3 GND Y 3 GND Y 3 IC Identification 7404 Inverter Chip 7408 AND Chip 7432 OR Chip

14.  IC Chip IC Chip Digital Logic Trainer • Complete diagram on page 98 • Breadboard • Points with a line through them represent the same connection line

15. Materials for Lab • Digital/Analog Trainer • 7432 2-Input OR gate IC • 7408 2-Input AND gate IC • 7404 Hex Inverter (NOT gate) IC • Hook-up Wire • Computer equipped with LabVIEW

16. Problem Statement • A farmer has two barns • A hen is free to move about. • A supply of corn is moved periodically from one barn to the other. • He wants to protect the hen from a predator fox, and also prevent the hen from eating the supply of corn. • An engineering student is hired to design an alarm system, using digital electronics. It will activate under the following conditions: • The fox and the hen are in the same barn. • The hen and the corn supply are in the same barn.

17. Problem Statement • Design a combination logic circuit that will accomplish this task. • The design should be cost effective, using the least amount of gates and input variables. • The logical output of the circuit should be connected to a lamp. • The lamp being “on” indicates alarm activation • The lamp being “off” indicates alarm deactivation. • The fox and hen and corn must be present in either barn 1 or barn 2 • Presence in barn 1=“1” • Presence in barn 2=“0”

18. Procedure • Truth Table • Determine what are the input variables and the output variable • Decide how many combinations there should be • Create and complete the truth table on a sheet of paper • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

19. Procedure • Boolean Expression • Gather all the combinations that produced a “1” for the output • Create a Boolean expression from these smaller expressions • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

20. Procedure • K-Map • Create a K-Map table • Be sure to only have one variable change states at a time from one box to another • Use the Boolean expression to fill in the “1’s” • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

21. Procedure • Simplified Boolean Expression • Use the K-Map to circle the pairs of 1’s • The 1’s may only be circled in multiples of 2, starting from the largest possible combination and working its way down • Write down the new simplified expression • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

22. Procedure • Logic Circuit Diagram • Use the new simplified expression to design a logic circuit • Have your instructor check your work • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

23. Procedure • Digital Trainer • Do NOT plug anything in until your instructor has looked over your work • Use the logic circuit and IC chip diagram to create the actual circuit on the breadboard • Be sure to connect each of the ICs to Ground and VCC - 5V • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

24. AND OR NOT Procedure • LabVIEW Simulation • With the use of your logic circuit diagram - recreate the circuit in LabVIEW • The front panel should have three control switches representing the variables and one Boolean indicator to represent the output • HINT: LabVIEW has the following built in comparison functions: • Truth Table • Boolean Expression • K-Map • Simplified Boolean Expression • Logic Circuit • Digital Trainer • LabVIEW Simulation

25. Written Assignment • Full Team Report (one report per team) • Use the guidelines on page 5 for help • Include original data with instructor’s initials • Original tables and work should be re-written so it is legible • Include a printout of the LabVIEW front and diagram panel • Include the topics found on the next slide • Remember to create a title page

26. Written Topics • Each of the following topics must be addressed in the full report and should be placed in the proper sections • What are possible applications of digital electronics? • Account for any error made during the lab • Compare the problem before and after it was simplified • What are some advantages of minimization using digital logic?

27. Recitation Topics • If your design did not work the first time, discuss why • Discuss how the digital circuit and its design would be affected if barn one had an alarm bell and barn two has an alarm horn

28. Closing • Return all the equipment back to your instructor