Project Overview
The purpose of the circuit designed in this project is to see which inputs will output in a Yes (1) or a No (0). The report explains if the vote will be a yes or no depending on who voted. If only two people voted yes and one is the president then the majority vote will be a yes. If only two people voted yes and neither are the president then the majority vote will be a no. One constraint in the project was you had to use two-input gates only.
Problem Conception
This truth table shows all the possible combinations of the four board member's votes. It also shows if the output of that combination will be a yes or no. The table shows that when there is a tie, whatever side the president is on wins the vote. The number of rows is equal to 2 to the fourth power because there are four variables in the circuit.
The un-simplified logic expression came from all of the combinations on the truth table that gave a 1 for the output. The expression is in the SOP form. Each of the minterms comes from the combination of each row that had a 1 in the decision column. I have my expression in the SOP form because it is easier to get from the table and personally it is easier to read than POS.
Un-Simplified Circuit
My circuit is in bus form because it made it easier for me to create it. There weren't as many crossing wires. You needed 4 inverters, 24 AND gates, and 7 OR gates. You would need 9 chips in the breadboard for the un-simplified circuit.
Boolean Algebra Simplification
This simplified Boolean Expression is making the expression easier to read and to wire a circuit.
Simplified Circuit
In my simplified circuit I used the bus form to make it easier to read and neater. I didn't have a resistor in the simplified circuit. The purpose of the resistor is to restrict some of the energy from flowing so that the LED doesn't burn up. In this circuit I needed 5 AND gates and 3 OR gates. I didn't need any Inverter gates. This came to a total of 8 gates. For this many gates I needed 2 74LS08 (AND gate) chips because each chip has four gates and I needed 5 gates to create the circuit. I needed one 74LS32 (Or gate) chip because I only needed 3 gates and one chip has 4 gates.
In the simplified circuit it contained many fewer gates and chips than the un-simplified circuit. The simplified circuit contained 27 less gates with only 8 gates rather than 35 gates in the un-simplified circuit. The simplified circuit also contained 6 less chips than the un-simplified circuit contained. This is important because it makes bread boarding and creating the circuit easier and much quicker. There is a lot less wiring to do, which means less mistakes you can make. Wiring the un-simplified circuit would be too hard and take way too long than breadboarding should.
In the simplified circuit it contained many fewer gates and chips than the un-simplified circuit. The simplified circuit contained 27 less gates with only 8 gates rather than 35 gates in the un-simplified circuit. The simplified circuit also contained 6 less chips than the un-simplified circuit contained. This is important because it makes bread boarding and creating the circuit easier and much quicker. There is a lot less wiring to do, which means less mistakes you can make. Wiring the un-simplified circuit would be too hard and take way too long than breadboarding should.
Bill of Materials
This is a table of the materials that went into the project showing how much of each material was used.