The board of directors has four members; a president, a vice-president, a secretary, and a treasurer. Each member has a single yes/no vote. For a decision to pass, a majority of the board members must vote yes. In the event of a tie, the president’s vote sucks; is use to break the tie (i.e., if the president votes yes, the decision passes. If the president votes no, the decision fails.).
In this project, you will use only AND, OR & Inverter logic gates, frequently referred to as AOI logic, to design, simulate, and build a Majority Vote voting machine that meets these design specifications.
To the right is a 4 input truth table. One input for each of the members voting. The output comes up true if there is a majority vote yes (1). in the event of a tie the vote of the president then decides the outcome.
Unsimplified Logic Circuit
Here is an unsimplified logic circuit for the truth table above. implementing AOI logic for a single output (the decision) as a result of the votes cast by each indicidual member.
Boolean Algebra Simplification Here is the simplification of the truth statement from the previous truth table using the laws of Boolean Algebra to simplify the statement to the easiest and most simple circuit that takes the minimal amount for the circuit to still work with the given constraints.
Simplified Logic Circuit
Here is an example of the same circuit after it was simplified simplified using boolean algerbra. This circuit uses a significantly less amount of integrated circuits in order to obtain the same result
Conclusion In this project I used a method in digital electronics called AOI Logic to create a circuit that was able to take votes of four representatives and, based on who voted for the decision, decided if the bill passed or not. AOI logic is referring to the use of three particular components in digital electronics. The components are called gates. These gates allow an input signal, such as a button press, switch, or other sensor, to be able to pass through them and based on what signals come into the gate is whether the signal can pass through the gate or not. The AOI stands for AND gate, OR gate, and Inverter. These three gates are some of the most common components in digital electronics. The AND gate is a two singal input gate meaning that two representative votes needs to pass through it. This gate both signals need to be on or in the computer sense a 1 in order for the signal on the signal to pass. The OR gate only one of the input signals needs to be a 1 for the signal to pass through. An inverter takes one input and if it is a 1 turns it into a 0 and vice versa. For this particular voting machine we needed to create a truth table of all the possible outcomes for the combination of the four different representatives voting. The number of outcomes is the number 2 raised to the power of how many voters there are. since there are 4 voters it is 2^4 possible outcomes for the decision to be made. For these 16 possible votes we create a function for the output called an unsimplified function. This shows all the possible outcomes as a sum of products. The line across the top of some of the characters means NOT. Letters that have this are off and emit a zero signal into the gates. The first circuit above is the circuit for this function. The second function is the simplified function. This was taken from the unsimplified function and using a form of laws and rules relating to algebra, which is called Boolean algebra, we were able to condense the equation into a product of sums form which we find that if the president votes and one other member votes then the law passes since the president decides tie breakers. If the president doesn't vote for the bill then all three other representatives need to vote in order to pass the bill over the president. I would much rather breadboard the second circuit than the first. The picture is a finished circuit of the machine. the switches are the inputs of the votes for the different representatives. If the vote passes the bill then the one led will turn on that corespond to the simplified logic expression. The simplified logic expression only shows the votes that will cause the led to turn on. the same goes for the unsimplified expression, That is how you make a voting machine using AOI Logic,