Tech 63 Lab 7 UTB6 V3 Simplification-1

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San Jose State University *

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Electrical Engineering

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Dec 6, 2023

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San Jose State University Aviation and Technology Department Tech 63: Analog and Digital Circuits Lab Number 7 Boolean Circuit Simplification Objectives: 1. To use Boolean theorems (Rules) to simplify logic circuits. Equipment/Material: This lab requires the use of a Multisim simulation software. Multisim software running on PC Digital Multimeter (DMM) 5 V DC Power Supply Pulse or Square-Wave generator Dual-Trace Oscilloscope LED 1 kΩ resistors (Quantity 4) Toggle Switches (Quantity 4) 7404 IC 7408 IC 7411 IC 7427 IC 7432 IC You could also select your logic gate from the “Place Miscellaneous Digital” menu. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Procedure In this experiment, you will experimentally use the basic rules of the Boolean Algebra to simplify logic circuits. +++++++++++++++++

Part I) Examine the logic circuit in Figure 1. Fig. 1 A. Write the Boolean expression for output: X= _______________________ Complete the expected output values in the truth table of Table 1. B. In Multisim, mount the appropriate logic gate(s) to the breadboard. Connect the inputs to Vcc, +5 V (using pull-up resistors) and GND (using SPST switches). Connect output to LED monitor. Verify the operation of your circuit by setting the toggle switches to each set of input values in Table. 1 and comparing the outputs observed to the corresponding outputs in the table. Play with different input values by toggling the switches and include two screenshots of your Multisim circuit one with LED “On” and the other with LED “Off.” C. On the electronic workbench mount the appropriate logic gate(s) to the breadboard. Connect the inputs to Vcc, +5 V (using pull-up resistors) and GND (using SPST switches). Connect output to LED monitor. Verify the operation of your circuit by setting the toggle switches to each set of input values in Table. 1 and comparing the outputs observed to the corresponding outputs in the table.

Play with different input values by toggling the switches and include two pictures of your breadboarded circuit one with LED “On” and the other with LED “Off.” Inputs Output A B C D A'B'C' AB'C' A'B'D X=A'B'C' + AB'C' + A'B'D (1 OR 0) LED Status (On or Off) 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 Table. 1 ++++++++++++++++ Part II) A. Simplify the output, X using Boolean theorems (Rules) to a SOP expression, and show the final result that includes three NOT gate, three 2-input AND gate, and One 2-input OR gate. Hint: Factor out B’C’ from in the first two terms of the original equation, then use the rule that A’+A=1, finally factor out B’ to find the final simplified expression. B. Using the simplified logic expression, construct the simplified circuit. Similar to Part I, include two screenshots of your Multisim circuit one with LED “On” and the other with LED “Off.” Using the Table. 1 as a starting point create another Table (Table. 2) to show and compare the output of the circuit in Part I to the circuit in Part II of this experiment. Also construct the simplified circuit on the breadboard and confirm the operation of the circuit. Include in your report the pictures of the simplified circuit one with LED on and one with LED off.

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++++++++++++++++++++++++++++ Part III) Compare the result of parts I and II and see if the outputs are the same. Make comment about the advantage of the simplified circuit. ++++++++++++++++++++++++++++ References: Include all your references. ++++++++++++++++++++++++++++ Lab Experiment write-up Format A written laboratory report for each experiment is required. The report must be neat, legible, and submitted in a typewritten form (use your computer). Use simple sentences that get right to the point and be specific The report should contain the following components:  Cover Page: This page includes the title of the experiment, the date, the course number, the course name, section number, and each team member’s name.  Objective: The objective tells what the experiment is all about. Write short sentences to explain the reasons for doing the experiment.  Equipment/Components: Write down the equipment and the components used for the experiment  Procedure: Write down the steps in a logical sequence to do the experiment.  Theory: The solution to the expected problem should exemplify the theory with calculations. All steps must be clarified with circuit diagrams. After you have solved the problem your next step will be to make a table showing all the parameters to be verified when you do the actual experiment. In other words, you simply want to verify your theoretical results or calculations in the laboratory.  Data: Your data must represent the experimental results.  Multisim screenshots: include the screenshots of Multisim for part I and part II with LED on and with LED off.  Pictures of the circuit on the breadboard: include the pictures of circuit on the breadboard for part I and part II with LED on and with LED off.  Conclusion: The conclusion tells what you accomplished. Did the experimental results agree with your expected results? © Mostafa Mortezaie