Lab Report Logic Simplification Using Boolean Algebra PDF

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Lab report for logic simplifications using boolean algebra...

Description

EET130 Digital Systems Instructor: Professor Gill

Lab 3 Logic Gates

Student Name(s):

Levi Parillo

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.

Levi Parillo

Date:

/11/2021

Adding your name here constitutes your agreement to the Honor Pledge as stated.

Cont e nt s Abstract.......................................................................................................................................................3 Introduction................................................................................................................................................. 3 Procedures...................................................................................................................................................3 Data:............................................................................................................................................................7 Conclusion...................................................................................................................................................9 References...................................................................................................................................................9

Abstract The purpose of this lab is to demonstrate how circuits work that are comprised of Boolean Expressions. It will demonstrate various Boolean Expressions and show how changes to the expression change the output of the circuit.

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.

Procedures 1. Write the Boolean expression for Y (the output of the Circuit 1 in Figure 1). AB+AC

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

5. Using Boolean algebra. reduce the expression in step 1 to its simplest Sum-of-Products (SOP) form: A(B+C) 6. 7. 8. 9.

Sketch the circuit for the expression found in step 5 (name this as Circuit 2). Write down the “predicted output” values for Circuit 2 in Table 2 for given inputs. Construct Circuit 2. 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

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

14. Using Boolean algebra. reduce the expression in step 10 to its simplest Sum-of-Products (SOP) form: -A(B+-C)

15. 16. 17. 18.

Sketch the circuit for the expression found in step 14 (name this as Circuit 4). Write down the “predicted output” values for Circuit 4 in Table 4 for given inputs. Construct Circuit 4. 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

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

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.

Da t a : Table 1: Circuit 1 results Input A

Input B

Input C

Predicted Output

Measured Output

0

0

0

0

0

0

0

1

1

0

1

0

1

1

0

1

1

1

1

1

1

0

0

1

1

1

0

1

1

1

1

1

0

1

1

1

1

1

1

1

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

1

1

0

0

0

1

1

1

1

1

0 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

1

1

0

0

0

1

1

1

1

1

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

1

0

1

0

0

1

1

0

1

1

1

1

1

0

0

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

1

1

0

0

1

1

1

1

1

1

0

0

Conclusion Upon completion of this experiment, there were a few topics learned. The first is how different Boolean Expressions can affect the outcome of a circuit. This lab also demonstrated that one can use Boolean Algebra to solve and predict the circuit outcomes. It is verified when the circuit is measured since the expected and predicted almost always are exactly the same.

References Floyd, T. L. Digital Fundamentals. [VitalSource Bookshelf]. Retrieved from https://bookshelf.vitalsource.com/#/books/9780134880068/...