Project Overview
The purpose of the circuit is to show our date of birth on the seven segment display. One constraint we had was you had to use one NAND and one NOR chip in your circuit. We used k-mapping to get our minterms for this project. Also you had to use common cathode.
Truth Table
The truth table shows every combination of the X, Y, and Z switches and what they are supposed to show on the seven segment display. It also shows which segments will be lit up based off the switches.
![Picture](/uploads/1/1/7/6/117626016/p113.png?250)
The
The a-g columns represents the segments on the seven segment display. An example of this is in the first row where b and c are on which creates a 1 on the seven segment display. The X's in the truth table can either be a 1 or 0, it doesn't matter.
Karnaugh maps and simplified logic for each of the seven segments
K maps work by taking the column of inputs from each letter to create the table. For labeling the K map the first two variables (X and Y) go on the left side and the third variable (Z) goes on the top. You fill it in order but switch the last two rows. You group it by grouping the 1's together in the largest groups possible that are powers of 2. If necessary you can group the 1's with X's. The expressions that you get from the maps are in the sum of products form. When grouping the 1's you look at the variables that label that column or row in order to get the minterm for that group. K-mapping is very efficient and easier than Boolean algebra in this case. There are so many expressions because each segment has it's own expression. This gives you seven expressions in total.
Multisim implementation
The image below shows my multisim; the wiring of my circuit. Each one of the circuits is the wiring for the segments in my seven segment display.
My circuit is in the bus form which makes it easier and simpler to wire. To create this circuit I needed 3 inverter gates, 4 AND gates, 4 OR gates, 2 NOR gates, and 3 NAND gates. I needed 5 chips to build my circuit. We ues NAND or NOR gates becuase it allows us to use all three of the AOI gates in 1 chip. By using a NOR gate instead of an Or and Inverter gate for C I was able to use 2 gates an 1 less chip in my circuit. Also by using NAND in my E gate I was able to use 1 less OR gate which led to 1 less chip. This is important because it makes it easier and faster to wire a circuit. in this project NAND and NOR didn't really simplify the circuit, it was just a requirement for the project. The seven segment display works by wiring a circuit to connect into each of the segments (A-G). There are two types of seven segment displays; they are common cathode and common anode. In Common cathode, which we used in this project, each segment is pre wired to ground so you need to wire power to each segment if you want to turn it on. Common anode works the opposite way in which it is pre wired to power and needs each segment wired to ground if you want to turn it on. We used common cathode in this because we had to. Also the digital logic board is already setup with common cathode so there is no reason not to. The resistors in the wiring limit the current going into the seven segment display. The common value of it was 200-270 ohms.
Bill of Materials
Here is the number of each component I used in creating my circuit
- Digital Logic Board - 1
- OR chip (74LS32) - 1
- NAND chip (74LS00) - 1
- Inverter Chip (74LS04) - 1
- AND chip (74LS08) - 1
- NOR chip (74LS02) - 1
- Wires- 100+
Bread-Boarding
I have placed all my chips and powered and grounded them. I also grounded and powered the board.
Me halfway through wiring and finishing the segments a, b, c, and d.
My finished project with all the wiring finished. It showing my date of birth.
My second breadboarding experience was a lot harder than the first. There were more circuits I needed to wire which meant more wires and it being harder. Also it was a lot more confusing because of following the wires and chips not being pushed in all the way. You need to pay attention to the NOR chips because they are opposite. One mistake I made was not pushing the chip in hard enough. A skill I learned is test every segment after you finish it.
Conclusion
One thing I learned from this project is to keep at it and don't let your mistakes discourage you. I also learned keeping your workspace clean makes it a lot easier. I wouldn't do that much different because my circuit worked without help, but I would color code the wires to make it look nicer and make it easier to read. I don't have any questions about the concepts. At first I was confused but throughout the project I realized how the seven segment display worked and how all the segments come together to make a number.