This circuit was designed to help with the United States 2000 Presidential Election between George W. Bush and Al Gore. The voting machine will allow the four board members to cast their ballots and will display the pass/fail status of each of their decisions. We could only use 2-input gates and if there was a tie, the president's vote would win.
problem conception via truth table & un-simplified expression
The table shows when the board members voted Yes(1) or No(0). The last column shows whether the decision fails(0) or passes(1). The rows are based on the number of variables. (2^x=# of Rows). In the case of a tie, what ever the president would vote on would win. If the president voted with anyone the decision would pass. The un-simplified expression was P'VST+PV'S'T+PVST+PV'ST'+PV'ST+PVS'T'+PVS'T'+PVST'. This is in a Sum of Products form (SOP). I got the minterms by looking at the purpose of the circuit and seeing what happens in a tie situation. The reason I chose SOP was because I used AND gates that led to OR gates.
In the un-simplified circuit we had to use 4 outputs. They were the President's vote, the Vice President, the Secretary, and the Treasurer. I used a bus because of how many gates we had to use. We had to use 24 AND gates, 7 OR gates, and 4 Not gates. You would you have to use 6 AND chips, 2 OR chips, and 1 Not chip.
boolean algebra simplification
This the Boolean Algebra Simplification. The final simplified form would be VST+PS+PV+PT
This is the simplified version of the circuit. It doesn't require a bus because there are not as many gates. You need 2 different types of gates, the AND gate, and the OR gate. We needed 5 AND gates, and 3 OR gates. Since we had 5 AND gates we needed 2 AND chips, and we only needed 1 OR chip. There are 4 gates in 1 chip. The simplified circuit needed less gates and chips. It need 16 less gates and 6 less chips. Its important to get less chips and gates because you will save money on every chip you get rid of. If you built the un-simplified circuit you would lose time and money.
majority vote circuitBill of materials
This is a list of the materials we needed to make the circuit on the breadboard.
The first picture is a view of my finished circuit. The second picture is a different angle of the circuit we had to create. The last picture is the breadboard with the materials you needed.
I made one error when making my breadboard circuit. I forgot to ground and power the chips. I've learned that using different color helps you see the different routes.
We learned how to breadboard during this project. When you started this project you needed to understand the problem statement and make a truth table based on it. When you make a logic expression, you need to see if it can be simplified with Boolean Algebra. You need to use Boolean Algebra so you can use less chip so it will be cheaper to produce. This was a fun project because we got to see how you go from the problem statement to a real life circuit you make.
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