Project Overview:
The purpose of this project was to create a voting machine. The machine is made from a series of wires and circuits on a breadboard that when an input is applied an outcome is achieved. The circuit had to make the inputs of majority vote turn on and also in the event of a tie, the president`s initial vote would break the tie. If the president did not vote then the output was not on. A main part of this challenge is to make the circuit with only 2-input gates.
Problem Conception via Truth Table and Unsimplified Expression
A truth table`s purpose is to show the possible input combinations and what the output for each will be. The number of rows in a truth table depends on the number of variables. To get the number of rows you take the number 2 and put it to the power of the number of variables. In this case there are 4 variables so the number of combinations is 16. (2^4 =16) In the event of a tie you can see that the output is on when the president's input on and off when the president`s input is off.
The unsimplified expression for this circuit was painfully long. The expression is set up in SOP format. To find out the unsimplified expression I took all the outputs in the truth table that were on and found the expression for each. SOP format was used because it gives a straight forward. With POS format it requires you to distribute the inputs to find out which output will be on.
The unsimplified expression for this circuit was painfully long. The expression is set up in SOP format. To find out the unsimplified expression I took all the outputs in the truth table that were on and found the expression for each. SOP format was used because it gives a straight forward. With POS format it requires you to distribute the inputs to find out which output will be on.
Unsimplified Circuit:
This circuit is in bus form. There are 4 7404 gates (NOT Gate), 24 7408 gates (AND Gates), and 7 7432 gates (OR Gate). This came out to a total of 1 NOT IC, 6 AND IC`s, and 2 OR IC`s. IC stand for integrated circuit.
Simplified Circuit:
The simplified circuit contained much less gates and IC units. This circuit required 4 less NOT gates, 19 less AND gates, and 4 less OR gates. this is important because it takes much less time to make but also requires less materials so the cost of the circuit goes down.
Boolean Algebra Simplification:
The simplified expression was VST+PV+PS+PT
These pictures show my breadboard at various angles so each and every wire's input and output can be seen and traced easily.