3.3 lab assignment

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ECPI University, Virginia Beach *

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120

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Electrical Engineering

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Feb 20, 2024

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EET130 Digital Systems I Instructor: Cameron Ruddy Lab 1 Signals and Number Systems Student Name(s): Brandon Walker Click or tap here to enter text. Honor Pledge: I pledge to support the Honor System of ECPI. I will refrain from any form of academic dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the academic community, it is my responsibility to turn in all suspected violators of the honor code. I understand that any failure on my part to support the Honor System will be turned over to a Judicial Review Board for determination. I will report to the Judicial Review Board hearing if summoned. Click or tap here to enter text. Brandon Walker Date: 2/11/2024 Adding your name here constitutes your agreement to the Honor Pledge as stated.

Contents Abstract ....................................................................................................................................................... 3 Introduction ................................................................................................................................................. 3 Part 1: Methods and Procedures .................................................................................................................. 4 Part 1: Results and Figures ...................................................................................................................... 4 Part 2: Methods and Procedures .................................................................................................................. 4 Part 2: Results and Figures ...................................................................................................................... 4 Conclusion ................................................................................................................................................... 5 References ................................................................................................................................................... 6 2

Abstract In this laboratory experiment, we aim to explore the intricacies of Boolean algebra by designing and implementing various example circuits. Boolean algebra serves as a foundational concept in computer science and electrical engineering, offering a systematic approach to analyzing and simplifying logic circuits. By leveraging Boolean laws and theorems, such as De Morgan's theorem and Boolean identities, we can manipulate logic expressions to streamline circuit designs, resulting in reduced component count, energy savings, and minimized time delays. Through practical exercises, this lab seeks to demonstrate how Boolean algebra techniques can be effectively applied in real-world circuit design scenarios, providing students with essential skills in digital logic optimization and efficiency. I ntroduction In this lab, we're learning about Boolean algebra by creating circuits. Boolean algebra helps simplify these circuits, making them use fewer parts and run faster. We use rules like De Morgan's theorem and Boolean identities to make the circuits simpler. This saves energy and time. Through hands-on activities, we see how to apply Boolean algebra to make circuits work better in real life. 3

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Part 1: Methods and Procedures EET130 Digital Systems I Lab: Logic Circuit Simplification Using Boolean Algebra I. Objective :  Build and observe functioning of various logic circuits. II. Parts List : Circuit 1  5 – AND gates  1 – OR gate  2 – NOT gates  1 – 1 KOhm resistor  3 – SPDT switches  1 – Digital probe  1 - VCC (5V)  1 - GND Circuit 3  4 – AND gates  1 – OR gate  3 – NOT gates  1 – 1 KOhm resistor  3 – SPDT switches  1 – Digital probe  1 - VCC (5V)  1 - GND Circuit 2, 4, 5 and 6  Number and types of gate as per your circuit  1 – 1 KOhm resistor  3 – SPDT switches  1 – Digital probe  1 - VCC (5V)  1 - GND III. Introduction: This lab will demonstrate the properties and illustrate some of the applications of Boolean algebra through the design and implementation of several example circuits. Boolean algebra is used to simplify logic circuits so that they are reduced to fewer components, saving energy and time delays in the circuit. IV. Procedures : 1. Write the Boolean expression for Y (the output of the Circuit 1 in Figure 1). ___________________AB+AC____________________________________________________ _______ 4

______________________________________________________________________________ 2. Write down “predicted output” values for Circuit 1 in Table 1 for given inputs. 3. Construct Circuit 1 shown in Figure 1 using components listed in parts list for Circuit 1. 4. For Circuit 1, change inputs A, B, and C using SPDT switches and observe output using digital probe connected to output. Write down “measured output” values in Table 1. If there are any differences between predicted and measured values, find the error and correct the problem. Figure 1: Circuit 1 Table 1: Circuit 1 results Input A Input B Input C Predicted Output Measured Output 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 5

5. Using Boolean algebra. reduce the expression in step 1 to its simplest Sum-of-Products (SOP) form: _____________________________________A(B+C)_______________________________ _______ ___________________________________________________________________________ 6. Sketch the circuit for the expression found in step 5 (name this as Circuit 2). 7. Write down the “predicted output” values for Circuit 2 in Table 2 for given inputs. 8. Construct Circuit 2. 9. For Circuit 2, change inputs A, B, and C using SPDT switches and observe output using digital probe connected to output. Write down “measured output” values in Table 2. These values should be same as predicted values. If there are any differences between predicted and measured values, find the error and correct the problem. Figure 2: Circuit 2 Table 2: Circuit 2 results Input A Input B Input C Predicted Output Measured Output 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 6

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1 1 0 0 0 1 1 1 1 1 10. Write the Boolean expression for Y (the output of the circuit in Figure 3). ______________________________________________A’+B- C=A(B+C’)________________________________ ______________________________________________________________________________ 11. Write down “predicted output” values for Circuit 3 in Table 3 for given inputs. 12. Construct Circuit 3 shown in Figure 3 using components listed in parts list for Circuit 3. 13. For Circuit 3, change inputs A, B, and C using SPDT switches and observe output using digital probe connected to output. Write down “measured output” values in Table 3. If there are any differences between predicted and measured values, find the error and correct the problem. Figure 3: Circuit 3 Table 3: Circuit 3 results Input A Input B Input C Predicted Output Measured Output 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 7

1 1 0 0 0 1 1 1 1 1 14. Using Boolean algebra. reduce the expression in step 10 to its simplest Sum-of-Products (SOP) form: _______________________________________A’(B+C’)____________________________ ________ ___________________________________________________________________________ 15. Sketch the circuit for the expression found in step 14 (name this as Circuit 4). 16. Write down the “predicted output” values for Circuit 4 in Table 4 for given inputs. 17. Construct Circuit 4. 18. For Circuit 4, change inputs A, B, and C using SPDT switches and observe output using digital probe connected to output. Write down “measured output” values in Table 4. These values should be same as predicted values. If there are any differences between predicted and measured values, find the error and correct the problem. Figure 4: Circuit 4 Table 4: Circuit 4 results Input A Input B Input C Predicted Output Measured Output 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 8

1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 19. Sketch the circuit for the following Boolean expression (name this as Circuit 5). Y = (A’BC + A’B’C)’ 20. Write down the “predicted output 1” values for Circuit 5 in Table 5 for given inputs. Figure 5: Circuit 5 Table 5: Circuit 5 results Input A Input B Input C Predicted Output 1 Predicted Output 2 Measured Output 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 9

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1 1 0 0 1 1 1 1 1 1 0 0 21. Using Boolean algebra. reduce the expression in step 19 to its simplest Sum-of-Products (SOP) form: ________________________________Y=A’(B’+C)________________________________ ___________ ___________________________________________________________________________ 22. Write down the “predicted output 2” values for this simplified expression in Table 5 for given inputs. 23. Sketch the circuit for the expression found in step 21 (name this as Circuit 6). Figure 6: Circuit 6 24. For circuit 6, change inputs A, B, and C using SPDT switches and observe output using digital probe connected to output. Write down “measured output” values in Table 5. These values should be same as predicted values. If there are any differences between predicted and measured values, find the error and correct the problem. Conclusion After finishing this experiment, several key learnings emerged. Firstly, we gained insight into how various Boolean Expressions influence circuit outcomes. Through hands-on experimentation, we observed the impact of different logical expressions on circuit behavior. 10

Additionally, this lab underscored the practical application of Boolean Algebra in analyzing and predicting circuit outcomes. By applying Boolean Algebra principles, we were able to solve circuit problems and anticipate their behavior accurately. This was confirmed through measurements of the circuits, which consistently aligned with our predictions, validating the effectiveness of Boolean Algebra in circuit analysis and prediction. 11