Boolean algebra has three basic logic functions and 3 derived logic functions. The basic logic functions are: AND, OR, and NOT. The three derived logic functions are: NAND, NOR, and XOR. In this lab we will just be manipulating 2-4 one-bit inputs: A, B, C, and D. Each logic function will compare these inputs and spit out a value based one the inputs. The AND function will output the value of A and B if they are the same value or it will output a 0 if A is different from B. The NAND function will see the inputs as not A and not B, and will output the exact opposite of the AND function. The others will follow the Table 1 below. Every electronic product today works by the complex arrangements of these 6 functions. One thing that helps us manipulate the logic functions is DeMorgans Law. This can be said by (A∙B)=A+B=A∙B and A+B=A∙B. The pictorial representations of these functions are in figure 1 below.
Table 1
Figure 1
AND NAND
OR NOR
NOT XOR
In this lab we built circuits that performed these basic functions. We were given the schematics of logic functions and they were labeled 74LS00, 74LS02, and 74LS86 for the NAND, NOR, and XOR logic functions, respectively. The chips that we use have 14 pins that have either a circular indentation or a U-shaped indentation that needs to be pointed toward the top of the board. Pin number one is located in the upper left hand corner of the chip. Pin numbers increase as you go down the left side of the chip. Numbering picks up on the other side of the chip in the lower right hand corner, and continues up the right side of the chip until it reaches 14 in the upper right corner. Pin 7 must be ground and pin 14 must be the power supply. To hook the circuit to the computer you must use a 50-pin connector that snaps into the breadboard. Power is located at pin 49 of the interface connector. Ground is located at pin 50 on the interface connector.
Once you have wired your circuit and made the power and ground connections you must make connections for the digital input and output. Pins 14-21 on the computer interface connector can be used to provide digital inputs to your circuit. Pins 22-29 on the computer interface connector can be used to view the digital outputs of your circuit.
Once the circuit has been connected correctly you will use a program called “Digital Lab” on the computer to analyze your circuit and confirm that it is connected correctly. Now you are finally ready to begin testing your circuit. To run the DAQ software push either the single arrow or the re-circulating arrow pair in the upper left hand corner of the DAQ window. To change the inputs use the hand tool to click on the switches for the input words 1 and/or 2. The output values are read like a bank of lights. When the light is gray, the digital value on that output line is a logic low (0). When the light is green the digital value is a logic high (1). To stop the program simply hit the stop sign button.
Procedure:
All the procedures in this lab have the same form. A circuit diagram is presented to us and we have to build the circuit and show it with a wiring diagram and a truth table. Truth tables are an efficient way to check and arrange your results.
Results:
The first circuit we built was a NAND circuit that was built using only NOR functions. The schematic looked like this:
A
Z
B
The wiring diagram looks like this:
Power
A
B
Z
Ground
When we tested the circuit it always gave us an output of 1 no matter what the inputs were. After verifying that it was hooked up correctly the lab instructor told us that we must have a bad chip. However, the outputs should have matched. The correct truth table should look like the NAND column not the Output column, which are the results we obtained:
Circuit 2:
We were given the following diagram and had to build it on the breadboard.
A
O1
O2
B
The wiring diagram looks as follows:
A Power
B
O1
Ground O2
Power
Ground
When we tested the circuit using the computer we obtained the truth table below.
Our solution matched the one that we did in our pre-lab on paper, on to the next problem.
Circuit 3:
The third circuit included NOR, XOR, and NAND functions. This was the most complicated one of the three to build and obtain the results. The circuit diagram that we were given was as follows:
A
B
C
Z
D
The wiring diagram for this circuit involved 3 chips and 4 inputs. There are many possibilities for building this circuit; the one we built looks as follows:
Power
Z
B
Ground
Power
B
A
C
Ground
Power
D
Ground
The truth table that we obtained when you used the computer program looks as follows:
The circuit again worked. The answers obtained by the computer program were exactly the same as the answers obtained in the pre-lab on paper.
Conclusion:
In conclusion this lab taught us the basics of building circuits and how to build circuits from picture. Now I know circuit logic and how it works both on paper and in a computer. Most importantly I learned the basics of the functions that build everything, that is, the AND, OR, NAND, NOR, XOR and NOT functions.
Laboratory 4:
Experiments with Digital Systems