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DOB Display
Project Overview
The circuit designed in the project displays my date of birth on a single seven-segment display. We used truth tables and Karnaugh mapping to simplify each expression that creates each number in my date of birth. This page will go through each step of the project, as well as the specifics of Karnaugh mapping, MultiSim, and bread-boarding.
Truth Table
The truth table shows which expressions are necessary to make each individual number of the date of birth. Using the truth tables we can derive each expression and then use the Karnaugh maps to get the simplified expression. Essentially the truth table is the start of the circuit designing process.
The X,Y, and Z columns show which arrangements of the switches will display each number of the DOB (F1). Then you see the a, b, c, d, e, f, and g columns which show when each segment should be on so that the right number is displayed. So, a 1 means that the segment is illuminated and a 0 means that the segment is not illuminated with the Xs showing that the last 2 digits don't matter, meaning they could be 1s or 0s and it wouldn't make a difference.
Karnaugh Maps
Above you see the Karnaugh maps for the circuit. These maps were created to help me simplify my logic expressions. K-mapping, as it is referred to, is not the only way to simplify logic expressions for there is Boolean algebra. However, I believe K-mapping is much more easier and dependable. The concept is pretty simple, but it requires you to memorize the process and create a K-map for each letter because of the 7 different segments in the display. So you create the K-map based on the number of variables. For this circuit, you need 8 boxes for each K-map. The first 2 variables go on the left and the third variable goes on the top. Taking the output column you divide the numbers into four groups. The four groups get inserted into the K-map in order left to right. But the 3rd and 4th groups are switched. Then you group the highest number of 1's and necessary Xs together and take the common variables that correspond with each. Continue this until there are no more 1s left. The final expressions derived from the K-maps are written in Sum of Products form.
MultiSim
Below you'll see the schematic diagram for the circuit. It contains the switches, bus, 220 ohm resistors, a NAND and NOR only circuit, as well as the accompanying gates and a seven segment common cathode display. Essentially, this is a virtual version of the breadboard that I built later on in the project. The major benefit of this is that I can test the circuit on the software easily before actually transferring onto the breadboard.
The circuit is in bus form, which allows it to be much more organized. There are three NAND gates, two NOR gates, three Inverters, and three OR gates needed. This translates to four chips (74LS00, 74LS02, 74LS32, 74LS04). I didn't really use NAND or NOR gates only for a specific circuit. But there would have been some benefits if I had done so. For example, some circuits, if built with NAND or NOR only, can require less gates due to cancellation. Less gates means less chips which means less money spent for each circuit. This allows for better efficiency and allows big companies to save lots of money. This also allows circuit builders and designers to save time, which is a very precious commodity.
As one can infer from the name, the seven segment displays are displays that are broken up into seven different segments that each light up when commanded to do so. There are two different types of these seven segment displays. There are common cathodes, which are grounded, and common anodes, which are powered. The cathodes, like the one used in this circuit, only light up a segment when that particular segment is receiving current. The anodes on the other hand, only light up their segments when the segment is not receiving current. In order to ensure that the bulbs for each segment don't receive too much current and blow, resistors are put into place.
As one can infer from the name, the seven segment displays are displays that are broken up into seven different segments that each light up when commanded to do so. There are two different types of these seven segment displays. There are common cathodes, which are grounded, and common anodes, which are powered. The cathodes, like the one used in this circuit, only light up a segment when that particular segment is receiving current. The anodes on the other hand, only light up their segments when the segment is not receiving current. In order to ensure that the bulbs for each segment don't receive too much current and blow, resistors are put into place.
Bill of Materials
This is a Bill of Materials stating the name, and amount, of the components needed/used in the project. The 74LS components are each different chips that act as different gates. These gates are needed for the bread-boarding of the circuit.
Bread-boarding
In the picture above you see the basics of a circuit. In other words this is the starting point. You see the chips necessary to create the circuit, the wires that power and ground the chips, and the switches being transported to an area with more inputs.
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This picture shows a circuit almost completed. As you can see there were lots of wires necessary, and it is not as simple/organized as the picture to the left. Four of the seven segments have been created and the other three are still left.
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Above is a picture of a much neater circuit. The wires were cut to the exact length needed, and they were pushed close the board. As neat as this circuit may be, it requires a lot more time and patience to build.
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All in all, I think my bread-boarding experience went pretty well. It wasn't as successful as my past breadboard circuits, but it was also not on the same level as complexity as the others. For this circuit we used two completely new chips that required different wiring. Thanks to the project, I learned how to wire these chips after making a number of mistakes. For instance, I failed to realize that the NOR gate chips were wired the opposite way the OR gates were wired. After tracing back the segments and looking at the chip diagrams I found my mistake and corrected it. All of the stress caused by the bread-boarding was definitely worth the new skills I acquired.
Conclusion
Looking back, there were some key things that I walked away with due to this project. I learned that K-mapping is actually a pretty useful and handy tool. It makes the simplification of expressions effortless. I also realized that MultiSim is really a circuit designer's best friend. It can prevent you from wasting a lot of time, and help you better understand what your circuit is meant to do. I also further developed my understanding of the seven segment displays, specifically the common cathode. Next time I do a project like this, I will be sure to manage my time more wisely, and take more time to create an organized circuit on the breadboard.
Bonus
Starting at the left we have the NOR only circuit that requires 10 gates. Then is the NAND only circuit which requires 15 gates. Finally, we have the AOI circuit, which surprisingly only requires 8 gates. This was really unexpected, but the AOI circuit, in terms of gates, is in fact the most efficient circuit for my DOB. But on the other hand the NOR and AOI circuits are tied in efficiency when looking at the number of chips needed. They both only require 3 chips.