The purpose of this project was too understand how NOR and NAND gates work and how to use and wire these gates on a breadboard to recreate our birthday. Some of the constraints were that we had to use only two input gates, using at least one NOR and NAND gate, and to complete the project on time and have the all the combinations working to achieve all points. This report will explain how I used the inputs a through g to make the outputs create my date of birth.
Truth Table
The truth table below is used to show the different combinations that were used in order to make the outputs needed. Truth tables provide a different way to create a logic expressions. After creating your truth table you can make a circuit and simplified logic expression.
Columns a through g represent seven parts of the seven segment display. They represent the outputs in the circuit. In this project I did not have to include dashes in my birth date. Due to this we included x's instead of dashes. These x's represent "Don't Care Conditions", meaning that it doesn't matter if the inputs are ones or zeros. I made the truth table so that it makes the simplest logic expression.
Karnaugh maps and simplified logic for each of the seven segments
K-Mapping is when you create the simplest logic expression. To make the simplest logic expression you first have to create a table with the outputs that you required from your inputs. The midterms are placed on the top and left of the truth table as you can see above. You can only change the inverted variables one at a time. You have to place the outputs based on the location of the midterms. Then you would group all of the on outputs in the least and most simplest way. Next you create a simplified midterm. All of the expressions are in Sums-Of-Product form. K-Mapping is much faster and easier to understand than Boolean Algebra. K-mapping also have a less chance of errors compared to Boolean Algebra . I have so many expressions because has to be seven segments in order for the circuit to work correctly and create my birthday.
Multisim
The image below is my Multisim circuit that I created. I used the bus so that the circuit requires less wires and to make the circuit less confusing. The inputs are X, Y, and Z and the outputs are a, b, c, d, e, f, and g. I used the Common Cathode SSD.
I used bus form for this circuit. I used a total of two 04 gates, one 32 gate, three inverters, and three 08 gates. Given the number of gates, I would need one 04 chip, one 32 chip, one inverter, and one 08 chip. In this project, we were required to use one NAND or NOR gate in the circuit. I used both a NAND and a NOR gate.I used a NAND gate for Segment a and I use a NOR gate for my segment f. We use NAND or NOR gates because it may be a much simpler and cheaper way to make a circuit. My circuit used fewer chips due to the simplifying. I used more chips then need though since I used both NAND and NOR gates but I still save chips by using NAND and NOR. This is important to know because it can allows the person making the circuit to save money and make the circuit as simple as possible.
The Seven Segment Display works through the logic expressions. Each segment has its own logic expression. Common cathode must be connected to ground and the segment must be connected to power. Common anode must be connected to power and the segment must be connected to ground. The common anode must be connected to power. We used the common cathode because it is easier to see a 1 as being on and a 0 as being off. The purpose of the resistor was to control the amount of current that flows into the Seven Segment Display.
The Seven Segment Display works through the logic expressions. Each segment has its own logic expression. Common cathode must be connected to ground and the segment must be connected to power. Common anode must be connected to power and the segment must be connected to ground. The common anode must be connected to power. We used the common cathode because it is easier to see a 1 as being on and a 0 as being off. The purpose of the resistor was to control the amount of current that flows into the Seven Segment Display.
Bills of Material
The bill of materials shows everything that I used. I used one AND, NOR, and OR chip and one inverter. MyDAQ is the device that I used to test my circuit. The ProtoBoard is the breadboard used to construct my circuit.
Bread-Boarding
I found my second bread boarding experience to be a lot easier then my first since I had a better understanding of how to create the circuit. A mistake I had was not knowing that one of my chips had backwards input and output spots. I learned that color coding is very useful because when you make mistakes like I did in my project it is very easy to locate and correct them. I used trouble shooting because some of my letters weren't working. I either found that the wire was just in the wrong hole or the wire was unplugged and color coding really helped me locate these problems.
Conclusion
This project taught me how to use a Seven Segment Display and how to wire a circuit to create my birthday. Next time I will trouble shoot through out the project so that it doesn't take as long to find multiple problems at the end of the project. I would find it interesting out engineers create chips and what everyday life objects use them. K-mapping is useful because it allowed you to create the simplified logic expression in few steps that are much less confusing than Boolean Algebra. Overall I thought this was a fun and very good learning experience as I learned a lot more about circuit and chips.