10/15/2015
The purpose of this project is to help perfect the Election process. In the year 2000 during the presidential election between George W. Bush and "Al' Gore. There was a controversy when George W. Bush won because of Florida's paper voting system, where certain peoples votes were counted more and some not counted at all, this project is to make an electronic voting system to insure this type of controversy doesn't occur again.
Problem Conception via truth table & Un-Simplified Expression
This truth table shows all possible outcomes for the vote. The variables are; President (P), Vice President (V), Secretary (S), Treasurer (T), and finally Decision (D). The numbers in the table are 1 and 0, 0 stands for the person voting no, and 1 stands for the person voting yes, and in the decision column a 1 means the decision has passed and a 0 means it has not passed. In the case of a tie, as seen in multiple cases in the truth table, whichever the President voted for goes, so if the president voted yes (1) then the decision would be passed, however if the president voted no(0) then the decision would not have been passed.
The Un-simplified logic expression shows all of the possible minterms. My expression is in Sums of Products form, and to get to this expression you must look at the truth table which shows the possibilities that can or cannot create a minterm of 1 (Passing vote) The expression only shows the passing votes possibilities, and to find those you simply look at the truth table and you express each row with a minterm of 1 in the expression format, which has variables with a no (0) with a dash over them, and those with a yes (1) without a dash.
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Un-Simplified Circuit
My un-simplified circuit includes a bus, a bus allows you connect inputs to there gates in a very organized way, so wires aren't everywhere and hard to follow. This circuit also uses a total of 24 AND gates and 7 OR gates and 4 NOT gates. This would need 1 Inverter Chip, 6 AND chips, and 2 OR chips.
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Boolean Algebra Simplification
Simplifying the expression allows to create a simpler circuit, cut cost, and make a more effective piece of equipment. Using Boolean Algebra (shown to the left) which is used to simplify circuit expressions by eliminating part of the expression that are unnecessary, making the circuit much smaller, and needing less gates, and or chips.
The Simplified Expression: PS + PV + PT + SVT |
Simplified Circuit
This is the Simplified circuit, this circuit has the same exact outcomes as the previous circuit, yet due to the Boolean Algebra Simplification, the circuit has become much smaller, and needs less gates. This circuit is also in bus form, which takes inputs and gets them to their gates in an organized way so there isn't so much cluttered wiring. for this circuit you need 5 AND gates and 3 OR gates, which is 2 AND chips and 1 OR chip.
Building the Simplified circuit saved 19 AND gates 4 OR gates, and 4 NOT gates. Which in turn leads to fewer chips needed. It is way more cost effective to build the simplified circuit, its also better because there are less components so there is a smaller chance of messing something up while making one. |
Bill of Materials
Component
1. Breadboard 2. LED 3. Resistor (330 ohms) 4. Circuit Board 5. AND Gates 6. OR Gates 7. AND Chips 8. OR Chips |
Quantity
1. One 2. One 3. One 4. One 5. Five 6. Three 7. Two 8. One |
Bread-boarding
This is a picture of my final breadboard, working on the breadboard is quite difficult and takes a bit of time. There are very many small details that you can miss place or forget entirely, so I figured out to take bread-boarding one step at a time, and then before moving on to the next part, check and make sure everything is where you want it, and then you can move on.
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Conclusion Paragraph
This project gave me a very strong understanding of how circuits worked, how to read circuits, and how to simplify circuits using Boolean algebra. Also to take all of that knowledge into the Multisim program and then to breadboard showed a wide range of different challenges in its own, from the small easy mistakes in bread boarding to connecting the right inputs and gates using Multisim, or simplifying an expression incorrectly and getting a completely different circuit. This project was completely start to finish in the sense that we did everything from identifying what we needed the circuit to do from the problem statement, to the truth table and then the un-simplified expression, then to the un-simplified circuit of our electronic voting device, and then using the Boolean algebra to create our simplified circuit.
Boolean algebra was very helpful because without it the circuit wouldn’t be able to be simplified, and the un-simplified circuit as seen above is much larger, much more complicated than the simplified circuit, yet the outcomes are the same. Simplifying the circuit also decreased the number of components completely which makes building the circuit much easier and much more readable to somebody else.
Some of the most important “take a ways” of this project is just to be very thorough while doing these sorts of things because there are so many mistakes that can be made, and easily missed, and learning how to go back and find those mistakes helped massively in creating the final breadboard.
Boolean algebra was very helpful because without it the circuit wouldn’t be able to be simplified, and the un-simplified circuit as seen above is much larger, much more complicated than the simplified circuit, yet the outcomes are the same. Simplifying the circuit also decreased the number of components completely which makes building the circuit much easier and much more readable to somebody else.
Some of the most important “take a ways” of this project is just to be very thorough while doing these sorts of things because there are so many mistakes that can be made, and easily missed, and learning how to go back and find those mistakes helped massively in creating the final breadboard.