Buy Logic Circuit Simplification Assignment

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).

______________________________________________________________________________

______________________________________________________________________________

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.

image1.png

Figure 1: Circuit 1

Table 1: Circuit 1 results

Input A

Input B

Input C

Predicted Output

Measured Output

Buy Logic Circuit Simplification Assignment

5. Using Boolean algebra. reduce the expression in step 1 to its simplest Sum-of-Products (SOP) form:

___________________________________________________________________________

___________________________________________________________________________

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

10. Write the Boolean expression for Y (the output of the circuit in Figure 3).

______________________________________________________________________________

______________________________________________________________________________

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.

image2.png

Figure 3: Circuit 3

Table 3: Circuit 3 results

Input A

Input B

Input C

Predicted Output

Measured Output

Buy Logic Circuit Simplification Assignment

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

___________________________________________________________________________

___________________________________________________________________________

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

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