Project Overview:
The purpose of creating the circuit was to create a majority vote machine for a board of directors. The constraints that were placed on us were that if there was a tie, the president's vote would act as a tiebreaker and that we only had two input gates to create the circuit. This report will show the majority of the steps that I took to create the circuit.
Problem Conception:
The purpose of a truth table is to make it easier to represent the possible inputs and outputs of an equation. You can calculate the amount of rows in the table by using the equation 2^x, where x is the number of variables. In this project we had 4 variables So there was 16 rows in the table. In this truth table we use a 1 to represents the idea passing and a 0 represents the idea failing. If there is a tie, the president of the Board's vote will decide if the idea passes or fails. So if there are two votes saying yes and two votes saying no, then the side which that the president votes on wins.
The un-Simplified equation of this circuit is D=PVST+PV'S'T+PVS'T+PV'ST'+P'VST+PV'ST+PVS'T'+PVST' . This is in sum of products form as all of the minterms are added together. I found the minterms by looking at my truth table and finding where the output was 1 . I then looked at the inputs, if the input was 1 I would just write down the letter.,ex. P, if the input was a 0 I would write down the letter with a line over it signifying it was not on. I chose to use sum of products equations as it was easier for me to derive the SOP equation from the truth table.
The un-Simplified equation of this circuit is D=PVST+PV'S'T+PVS'T+PV'ST'+P'VST+PV'ST+PVS'T'+PVST' . This is in sum of products form as all of the minterms are added together. I found the minterms by looking at my truth table and finding where the output was 1 . I then looked at the inputs, if the input was 1 I would just write down the letter.,ex. P, if the input was a 0 I would write down the letter with a line over it signifying it was not on. I chose to use sum of products equations as it was easier for me to derive the SOP equation from the truth table.
Un-Simplified circuit:
I put my Un-simplified circuit in bus form, In an attempt to simplify the wires in the circuit. Then the wires connect on the other side of the bus. The circuit contains in total 35 gates: 7 OR gates, 24 AND gates, and 4 inverter gates. If you were to make the circuit, you would require: 2 OR chips, 1 inverter chip, and 6 AND gates.
Boolean Algebra:
The Un-simplified equation for the circuit was D=PVST+PV'S'T+PVS'T+PV'ST'+P'VST+PV'ST+PVS'T'+PVST', and after being simplified down was D=PV+PT+PS+VST.
Simplified circuit:
For my Circuit I didn't use bus form as the equation wasn't very complex and was quite easy to see where the wires were going unlike the un-simplified circuit. The simplified circuit only required 5 AND gates and 3 OR gates, which is a lot less than the un-simplified circuit with 7 OR gates, 24 AND gates, and 4 inverter gates. when we made this circuit it only required 2 AND chips and 1 OR chip. I knew this because each AND and OR chip has 4 gates, so 5 AND gates requires two chips and 3 OR gates requires one chip.
The simplified circuit is justified because it makes the circuit a lot more simple, as it only requires 3 chips instead of the 9 that the un-simplified one would. The circuit being more simple is important as it means you need less materials and that the circuit board will be a lot easier to comprehend. Also if you were to create this for a company they would want you to make the simplest possible circuit as it would cost less.
The simplified circuit is justified because it makes the circuit a lot more simple, as it only requires 3 chips instead of the 9 that the un-simplified one would. The circuit being more simple is important as it means you need less materials and that the circuit board will be a lot easier to comprehend. Also if you were to create this for a company they would want you to make the simplest possible circuit as it would cost less.
Bill of Materials:
This is a list of the amount of materials that were used in making the breadboard. I was surprised by the amount of materials used in the simplified circuit compared to the un-simplified ones
Bread-boarding:
My bread-boarding experience went pretty badly. I was very slow in wiring and had trouble finding the right place to put my wires. I had many problems figuring out where to place the president, vice president, secretary, and treasurer cables. I also accidentally placed 2 of my chips in the wrong place. this part of the project took me a couple of hours for me to get my my circuit to work. But most of this time was spent with the chip in the wrong place. The skills I learned from bread boarding were that organizing the wires and making sure the chips are places right is very important to getting your breadboard to work
Conclusion:
This project showed to me that I need to get better at understanding how to simplify circuits. I was having some trouble trying to figure out which theorem to use to simplify my equation. I realize how important it is to understand how to simplify a circuit that was as complex as the un-simplified circuit. If I was not able to simplify it I would have been stuck with a complete mess when I was bread-boarding. the Boolean algebra part was what held me up the must, which is unfortunate as it was a very important part in being able to simplify it. This project was good for teaching us how to go from basic information to a completed circuit board. The process that I followed to create my circuit was: First I created a truth table and then I derived an un-simplified logic expression. Then once I did that I checked to see if there was any way to simplify the equation down to a less complex circuit. Then I checked to see if the two equations were equivalent. Then all that was left was to wire the circuit, which gave me a lot of trouble when I was doing it. I felt it was difficult for me to focus on the circuit and was easily distracted, losing my train of thought and where to place the wires.