Majority Vote
Project Overview
The purpose of the circuit designed in this project is to better help us understand how to breadboard, how to actually apply our knowledge of Boolean algebra in an actual circuit, help us practice Boolean algebra, and how to take a circuit drawn on paper or made in multisim and build it on a breadboard. while only being able to use two-input gates. In the event of a tie the president's vote decides whether or not the vote gets passed or not.
Problem Conception via Truth Table & Un-simplified Expression.
The purpose of the truth table is so that you can see the inputs and outputs, so that you can start to create a formula in SOP format. After that you then can start to simplify it using Boolean algebra. In this truth table if there is a tie in votes, then the president's vote is the tie breaker. Otherwise the majority vote gets passed. In this table there are 16 different input combinations. This is because for every different factor (P,V,S,T) doubles the number of combinations, represented by the formula; 2^f. Where f represents the number of factors.
The un-simplified expression for the project is M=notPVST+PnotVnotST+PnotVSnotT+PnotVST+PVnotSnotT+PVnotST+PVSnotT+PVST. This un-simplified expression for the project is just telling you all of the inputs where the vote gets passed. i arrived at each of these minterms by inputting values to see which ones would work. I used SOP form, because it is easier to look at and compare to everything else, and in my opinion it is easier to simplify than POS form.
Un-Simplified Circuit
The circuit above is in bus form. It has been somewhat organized so as to be able to spot errors easier. There are 24 AND gates, 7 OR gates, and 4 Inverters. This circuit would take 6 08 chips, a 04 chip, and 2 32 chips.
Boolean Algebra Simplification
After factoring out some values from the un-simplified expression, then using most of the Boolean algebra theorems I was able to simplify the expression down to just M=PV+PS+PT+VST.
Simplified Circuit
The circuit above is in bus form. There are 5 AND gates, 3 OR gates, and no Inverters are needed. this circuit would only need 2 08 chips and a 32 chip. No 04 chips, because there are no inverted factors in the simplified expression, only 2 08 chips, because there are 4 gates per 08 chip and there are 5 AND gates, and 1 32 chip, because there are 4 gates per 32 chip, and there are only 3 OR gates.
The simplified circuit contains 23 less gates, and 6 less chips. This is important, because if you were to try and build either of these circuits, you would want to build the simplified. The simplified would be a lot easier to build, and would use less parts. If you were to build the un-simplified circuit, you would be wasting time and resources, because you get the resulting circuit for less time and resources when you build the simplified circuit.
This table represents the amount of the materials required, are needed to build the simplified circuit. The table above shows the number of AND gates, Or gates, Inverters, 04 chips, 08 chips, and 32 chips.
Bread-boarding
In these pictures you can see that I used color coding and made sure that the majority of the wires were just the right length. Yellow represents the President, Red represents both positive wire connections and the Vice President, white represents the Secretary, blue represents both ground wire connections and the Treasurer, black represents minterm connections, and the green wire is just a different color taking the expression to the resistor so that it is a little more spaced out and neater, plus it's just a random color so I don't get confused to where it's supposed to go.
As my first breadboarding experience I made many mistakes. I had to make a second breadboard, because I didn't feel like trying to figure out what was wrong with my first breadboard that was completely un-organized and just a mess. so I made the second one and decided to try and make it as neat as possible, however I was a little rushed for time when I was building my second breadboard, so I just started using one color and stopped looking for wires that were flat to the board. In this project I learned breadboarding skills, how to simplify complex expressions using Boolean algebra, and how important neatness is.
Final Project Conclusions
After completing this project I have learned many different things. Including the ability to convert a circuit onto a Bread-board, how to simplify complex expressions using Boolean algebra, the importance of neatness, and the importance of color coding the wires. This project helped me see just how important it is to simplify expressions before even trying to build them. This project shows us how to apply the skills that we have been taught over the past few weeks. When I was first given the project, I first made a truth table, and then used common sense to fill it out. From there I was able to find the un-simplified formula using the truth table. I then used Boolean algebra to simplify the expression. Then I went onto Multisim and made both the simplified and un-simplified circuits. After I finished both circuits on Multisim I started the construction on my Bread-board and used the simplified expression as a reference trying to replicate it onto the Bread-board itself. Boolean algebra is useful, because without Boolean algebra I wouldn’t have been able to simplify the expression and the Bread-boarding process would have taken a lot longer than it did with the simplified circuit. Overall this was a fun, hands on project that had many benefits and helped me understand so much about Boolean algebra and Bread-boarding.