Project overview
In this project we are trying to create a circuit to represent the decisions of the President (P), Vice President (V), Secretary (S), and Treasurer (T). Some of the constraints are as follows:
- If the majority vote yes then the output is yes or 1
- If it is a tie, the president has to be in the vote for it to be yes (PV) or (PS)
- We also only have 2 input gates
Problem Conception
This is a truth table. The purpose of a truth table is to help you find the equations for when the output is one, or in this case, when the vote is yes. There are a total of 8 combinations where the vote is yes, indicated by the 1. There is a relationship between the number of variables and the number of rows. If you have 4 variables, like we do here, you raise 2 to the number of variables, giving you the number or rows. If you look at the table you will see that it meets the constraints because ST is a tie but still has an output of 0, while PT has an output of 1.
This Un- simplified version of the expression is in SOP form. I arrived at the midterms buy looking at the columns where the output is one and added the midterms together. I used created a SOP expression because it is easier to read and work with.
Un-Simplified Circuit
This is the un-simplified circuit of the expression. As you can see it is very complicated and unnecessary. There are way to many wires and if not for bus, it would look worse. This model of the circuit is in bus form. To make this model on Multi-sims, I had to use 24 AND gates, 7 OR gates, and 4 NOT gates. You would need 1 inverter chip, 6 AND chips, and 2 OR chips.
Boolean Algebra
Simplified Circuit
This is the simplified version of the circuit of the expression. It looks and is way more simple than the un-simplified circuit, which makes sense. This is in bus for as well. The purpose of the resistor before the light is to resist the flow of electricity from the batter to the light to prevent the light from getting too much voltage and blow it. You need 5 AND gates, 3 OR gates and 4 NOT gates. Each AND and OR chips have 4 gates in each, that means that you would need 2 AND chips and 1 Or chip. A NOT chip has 6 gates so you would only 1. This circuit definitely has fewer gates and therefore it would require fewer chips. The simplified circuit has 5 less circuits in it. This is important because it could greatly reduce the cost of the mass production of a device that uses this circuit.
Bill of Materials
This is the bill of materials chart which explains how many of each item is required to make the circuit.
Bread-Board
In this picture it shows the breadboard before it had any wires or chips.
In this picture I am currently working on the breadboard midway to completion.
This is the completed circuit, tested and working.
My first bread-boarding experience was pretty good. I did to run into one problem though. when I first went to go check my board, it did not work. I had to go back and look to see where I went wrong and i saw that I had connected the resistor-light set up wrong. After I had fixed this my board worked and i was able to prove how the expression worked in my circuit. One of the skills I learned is to bridge the positive to the positive and the negative to the negative.
Conclusion
I had a lot of take-aways from this project. I had fun doing this project and would enjoy doing it again. In this project I learned how to improve my Boolean algebra as well as how to make the simple expressions that we work with, in real life with a bread board and circuit chips. This project shows a circuit representation of a majority vote scenario between the board of directors. There are some conditions stated that would be used in the situation of a tie. For example, the vote will only go through with a yes if 3 out of the 4 members, or majority vote, vote a yes. If it happens to be a tie then the president has to be one of the 2 votes of yes for the vote to pass through. When going from a problem statement to a finished circuit design you need to first make sure that the expression is in its most simplified form. Then, have to analyze the expression in order to figure out how many gates are needed which will tell you the number of circuits you need. Finally, you just wire the bread board and test out the circuit. Boolean algebra is important because it allows you to simplify an expression. You can use that simplified expression to make a more efficient circuit.