Majority vote
I needed to make a circuit that would ensure the decision reliable and accurate. The board of directors has four members: president, vice-president, secretary, and treasurer. Each member has a single vote and In the event of a tie president's vote is use to break the tie.
truth table
By constructing the truth table, we can easily see what happen that will make the decision a yes. To make a decision yes, only possibilities are president with other member/s or all of the members except for the president. On the truth table, the number of rowd are depend on the number of the variables(2^n).
un-simplified logic expression
The un-simplified logic expression shows all the different possibilities that there can be a decision. The circuit is put into sum of products form and the decision is output as 1. I choose to use the sum of products form since it is easier comprehend than product of sums.
un-simplified circuit
I created my un-simplified circuit with long way. Using 4 invertor gates, 24 AND gates, and 7 OR gates, I used the circuit to recreate the truth table and make the correct decisions where the diode would light up. Given the amount of gates, it would take 8 chips to make the circuit on a breadboard.
boolean alegebra
Using the boolean alegebra, I was able to simplified the original expressions to simpler and smaller form
simplified circuit
The simplified circuit is used instead of the original circuit to make it easier on the person making it and to save money. In the simplified version there are 5 AND gates, and 3 OR gates. since every chip can hold 4 gates at the most, I would need total 3 chips, 2 for AND gates and 1 for OR gates.
Compared to the un-simplified circuit, there is 4 less invertor gates, 19 less AND gates, and 4 less OR gates. Also the simplified circuit contains 5 less chips. Simplified circuit is more beneficial, because it is much easier to understand and put together.
Compared to the un-simplified circuit, there is 4 less invertor gates, 19 less AND gates, and 4 less OR gates. Also the simplified circuit contains 5 less chips. Simplified circuit is more beneficial, because it is much easier to understand and put together.
bill of materials
The first column shows the components and the second column shows the quantity. I used these materials to build a simplified circuit on the breadboard.
breadboard
This is the finished product of the circuit. It shows all wires, chips, and LEDs used and where they are placed.
This are the 3 chips used to complete the circuit. There are 2 AND gate chips (74LS08), and 1 OR gate chip(74LS32) .
This shows the connection between the rest of the circuit and the LED.
My only mistake was I didn't connected wires from e to f. Overall, I did well throughout building the circuit.
This are the 3 chips used to complete the circuit. There are 2 AND gate chips (74LS08), and 1 OR gate chip(74LS32) .
This shows the connection between the rest of the circuit and the LED.
My only mistake was I didn't connected wires from e to f. Overall, I did well throughout building the circuit.
conclusion
Things that I take out of the 2.1.1 Majority Vote Project is how to represent a AOI expression from a word problem and use it to create a truth table, logic expressions, and real life circuit to use for the particular problem. This problem involves a candidate voting system including a president, vice president, secretary, and treasurer. It states that we needed to create a voting system where each person has single votes and if there are 3 votes for yes the decision is a yes. The decision is also a yes if there a tie where two people vote yes and two people vote no and the president votes yes. For example, if the president and treasuer both vote yes then the decision is a yes but if the secretary and treasurer vote yes then the decision is a no. Because, decision is yes when President and other member or 3 other members based on my simplified logic expression. Finding the un-simplified expression was the easy with the truth table. After that I had to use boolean algebra to simplify it. It helps the designer save time and money when making the circuit by using less materials and AOI chips. This project gave me a better understanding of relating real world problems into circuits and logic expressions.