Boolean Function/Fundamental Operations

Student Information

Part 1. Objectives

• To utilize the fundamental operations of Boolean algebra I the logic - circuit measurements.
• To investigate the equivalence of Boolean expressions experimentally.

Part 2. Equipment and parts required:

• 2 OR gates, 2 - input '32 or equivalent
• 3 AND gates, 3 - input, '11 or equivalent
• 2 inverters, '04 or equivalent
• 1 power supply. 5 Vdc
• 1 VOM

Part 3. Procedure

1. Construct the logic circuit in the figure below. Use 0 = 0Vdc and 1 = +5Vdc, measure the output voltage levels to complete the table.

Inputs			Output
A	B	C	x
0	0	0
0	0	+5
0	+5	0
0	+5	+5
+5	0	0
+5	0	+5
+5	+5	0
+5	+5	+5

2. Construct the logic circuit below. Use 0 = OVdc and 1 = +5Vdc, measure the output voltage levels to complete the value of x in the truth table. Use the measured output voltage from a 2 - input OR gate as shown to complete the y column in the table. Are the two circuits equivalent? (yes or no)


Inputs		Output
A	B	x = A + A'B	y = A + B
0	0
0	+5
+5	0
+5	+5

3. Construct the logic circuit below. Use 0 = OV de and 1 = +5 dc, and use the measured output voltage level to complete the value of x in the truth table below.

Inputs			Output
A	B	C	x	y
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

4. Construct the logic circuit shown in Figure below (a) use 0 = OV dc and 1 = +5 V d, and record the output voltage levels to complete the values of x in the table below. Similarly, construct the circuit in Figure below (b), and record the values for y by perfect induction, are the two networks equivalent? _ Note the 2 - input OR gates to construct a single 3 - input OR gate in Fig. 4 - 4c.


Inputs			Output
A	B	C	x	y
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

Part 4. Questions

1. Write the Boolean expression for the middle AND gate in item no 4 figure (a) and evaluate its output for A = 1, B = 0 and C = 1.

2. Write the Boolean expressions for the output x in item no 4 figure (a) and y in item no 4 figure (b)

3. Using the result from step 5, explain whether or not a '10 NAND gate will function as an inverter if the unused inputs are left unconnected.

4. Use proof by perfect induction to prove or disapprove the equivalence of x = ABC + ABC + ABC + ABC + ABC AND y = AB + C.(upload your solution)
Press this to download