Majority vote
We designed the simplified circuit so that we could get the same majority vote outcome without using the enormous simplified version. Since there were only four variables, if there was a tie then the vote would depend on if he president voted or not. Any vote that the president voted for would pass, unless everybody else voted against. The simplified equation turned out to be D=VST+PV+PS+PT.
unsimplified equation/circuit
This is the truth table used to initially get the unsimplified version. I knew that I needed to have a 5X16 table because there are four variables with a decision, and 2^4= 16. This table shows the decisions in different scenarios of voting
Here is the unsimplified equation, which I found by seeing which combinations give me an output of 1. (1-Pass, 0-Fail)
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This is the unsimplified circuit which I made on MultiSim software. I used twenty-four 74LS08D (AND) gates and seven 74LSD32D (OR) gates. I had finished the circuit before I was informed that there is a component called "BUS" which condences all the wires and makes it much easier to work with and to troubleshoot.
simplified equation/circuit
![Picture](/uploads/3/9/1/8/39189363/published/p141.png?1489779733)
Here is my Boolean Algebra from which I determined the simplified equation. I had to use many theorems to make sure that the equation could not simplify any more.
This is my simplified circuit, which as you can see is a lot easier to look at and interpret. I only used 5 AND gates, and 3 OR gates. Since it was already a condensed equation, I did not need to use the BUS component.
Bill of materials
Breadboard
conclusion
This was the first time that I had ever dealt with AOI logic expressions and using most of these materials. I thought that this was a great learning experience for me. It was a very fun project even though I got frustrated with the lengthy process of the unsimplified circuit and trying to figure out the Boolean Algebra theorems. From start to finish I made a couple of mistakes, such as not using the BUS component, which would've made the unsimplified circuit much easier to troubleshoot. It also took me a while to complete my actual circuit on the breadboard, which was a very tedious process. After all, I am glad I got the opportunity to work on this project as I learned a lot from it.