Project Overview:
The purpose of the circuit is to determine the different outcomes of 4 people voting on board members. The circuit could only use2 imput gates. When there is a tie then the president’s vote is the deciding vote. This project explains how the use of Boolean algebra can make a very long output expression much simpler.
Problem Conception via Truth Table & Un-simplified Expression
The truth table shows all of the possible outcomes with all the possible inputs. The PVST are the different board members and each column has every possible vote. 1=Yes and 0=No, when it is a tie the output is decided with the vote of the President who is P. The number of variables corresponds to the number of rows by the how many variables is the number of rows, 2 variable is 4 rows, 3 variables is 8 rows, 4 variables is 16 rows. Each variable you add you multiply the number of rows by 2.
The unsimplified expression is in Product of Sums form. It is easier to simplify and make a circuit in this form. I got this expression by looking at the minterms on the truth table and writing down the inputs as p or not p and so on, then add them all in the expression. There are 8 outcomes with a 1 with the 16 imp;uts.
Un-simplified Circuit
This is the unsimplified version of the circuit and it looks very messy, each gate is used to put the expression into sum of products form. I was only allowed to use 2 imput gates which made the circuit much messier and more tedious to make. 4 inverter gates, 23 and gates, and 8 or gates. 1 inverter chip, 2 or chips, and 6 and chips so total of 9 chips to build the circuit.
Boolean Algebra Simplification
This is the simplified expression after completing the Boolean algebra.
Simplified Circuit
This is the simplified circuit, it uses only 5 and gates and 3 or gates. 2 and chips and 1 or chip. 3 chips to build the circuit. I did this by counting the number of each gate and each chip takes 4 gates, 5 and gates is 2 chips, 3 or gates is 1 chip. The simplified circuit contained much fewer gates the unsimplified contained 35 gates, the simplified contained only 8 gates. The unsimplified had 9 chips and the simplified only has 3 chips. This is important because the fewer amount of chips lowers the cost of the circuit.. If you build the unsimplified then you would be spending much more money on chips and hardware.
Bill of Materials
2 AND chips
1 OR chip
Power source
resistor
LED
4 switches
Wires
1 OR chip
Power source
resistor
LED
4 switches
Wires
Bread-Boarding |
Here every thing is being connected to the power source
Here i am connecting the switches to the correct chips
Here everything is complete and the LED and resistor are in place
Tinkercad is not very fun to use, i had trouble with the circuit because the software is not user friendly.
Tinkercad is not very fun to use, i had trouble with the circuit because the software is not user friendly.
Conlusion
The takeaways from this project are being able to see how circuits can be simplified using skills of Boolean algebra to simplify the expression. Also, going through stressful situations and getting frustrated, trying to figure out where your circuit went wrong. This project shows the job of simplifying circuits and how tedious it can be. The basic process is first making the truth table and then make a AOI logic aexpression. It is easier to put it into sum of products form. Then you can simplify that expression using Boolean algebra and using the simplified expression make the final circuit. The Boolean algebra is useful because simplifying the expression can cut costs for chips and wires, also it is much easier to work with when making the circuit.