Introduction to Digital Logic Lab 1: Simplification of Boolean Functions Introduction In this lab you will build circuits that demonstrate the relationship between a Boolean function, the truth table, the logic diagram, and the measured values when the circuit is implemented. For each circuit, the laboratory is divided into three parts: design, schematic/simulation, and implementation/testing. The first part may be done by hand, the second part of the lab will require the use of Multisim (or equivalent circuit simulator). In the third part, you will build the circuit using discrete ICs in the Digital Circuits Laboratory. Your circuit diagram and Multisim simulation will be demonstrated in the Laboratory on Thursday. This laboratory exercise should be completed pairs. Significant collaboration between project teams is not expected. Original and Simplified Functions Given the following original Boolean functions, show that the original and simplified circuits behave the same way. Be sure to use the distributive theorems. 𝑭 = (𝒙′ + 𝒚 + 𝒛)′ + 𝒙′ + 𝒛 Pre - Laboratory Assignment 1. Design: The goal of the design step is to understand the behavior of the circuit. This usually involves deriving the truth table for the function. a. Circuit 1 (original): Derive the truth table. 1 2. 3. 4. 5. 6. b. Circuit 2 (simplified): Simplify the function algebraically. Derive the truth table. Schematic and Simulation: The goal of simulating the circuit is to confirm that the circuit behaves as designed. Draw both the original and the simplified logic diagram in MultiSim. Generate a simulation output using the logic converter tool in Multisim. Verify that the output of Circuit 1 and Circuit 2 corresponds to the truth table you derived in part 1. Building Circuits: Prior to completing the lab, watch the following videos that will prepare for the lab. 1) https://www.youtube.com/watch?v=Ynxg19lEkvg and 2) https://www.youtube.com/watch?v=XAUmPEICX00 Implementation: Once a circuit is simulated, it can be built using integrated circuits and verified using the truth table. Build the original and simplified circuits on a breadboard. Use an LED connected to a resistor to indicate the output of each circuit. Testing: To test the circuits, apply input voltages that correspond to the each row of your truth table. Observe that the LED provides the expected output. Print Grading Rubric: Bring a copy of the attached grading rubric to class (one per group). What to bring to lab demonstration: 1) Circuit 2 - simplified circuit, 2) Truth table for original and simplified circuit, 3) MultiSim simulation for original and simplified circuit, 4) Circuits for the original and simplified circuit that have been built and tested. Lab Safety: Students are encouraged to work with a partner and observe safe laboratory practices when building circuits. The labs for this course use low power sources, so be sure to verify the voltage settings on the power supply. Build your circuit before connecting to the power supply. Be aware of factors that cause overloading of the power supply and/or components overheating. Build your circuits using dry hands and on dry surfaces. Remove jewelry and avoid using conductive objects near circuits. Do not eat or drink in the laboratory. Electrical circuits can be hazardous, producing tingles (> 1 mA), shocks (> 5 mA) and electrocution (> 100 mA) so safety is critical. Please contact Mr. Andre Lewis, Laboratory Technician, with any lab safety concerns. Laboratory Report What to Turn In A laboratory report should be submitted, detailing your pre-laboratory assignment and the implementation of the circuit in the lab. The report must include standard sections such as 1. Cover Page 2. Objective: Indicate objective(s) of the laboratory exercise, in your own words. 3. Equipment and Components 4. Introduction: Background on the lab including approach selected. 5. Procedure: Provide the steps taken to complete the lab. 6. Design, Theory and Simulations: Include your design, steps to simplify equations, Multisim schematic, and simulations. Results in this section should be compared with your implemented circuit and any differences must be discussed. Be sure to include: documentation of your design process (two truth tables), screenshots of your two schematics with the simulation output shown 7. Results and analysis: Discuss the results from building and testing your circuit. 2 8. Conclusions: Indicate how well you met the lab objective(s). Did your simulation and circuit behave the same way? Did the original and simplified circuit yield the same results? What things did not work and why? What could you have improved? 3 Simulation Instructions Displaying a Truth Table using a Logic Converter To use the instrument, click on the Logic Converter button in the Instrument toolbar and click to place its icon on the workspace. The icon is used to wire the Logic Converter to the circuit. Double-click on the icon to open the instrument face, which is used to enter settings and view measurements. The Logic Converter is able to perform several transformations of a circuit representation or digital signal. It can be attached to a circuit to derive the truth table or Boolean expression the circuit embodies, or to produce a circuit from a truth table or Boolean expression. 4 Introduction to Digital Logic Lab 1: Simplification of Boolean Functions Date: ___________________ Name: ______________________________________________________ 1 2 Circuit 1 (8 points) • Design • Schematic • Simulation • Implement Original • Implement Simplified Troubleshooting Discussion of results (2 points) Total 5 Total Comments
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