Date of birth Project
Overview
The purpose of this project was to create a circuit that would, when certain switches were flipped, display each of the 6 numbers of my birthday. It would be displayed on a cathode seven segment display so each of the segments would have its own circuit.
Truth Table
This is the truth table for the 7 segment display. Its purpose is to more easily represent the possible inputs for the circuit, with x y and z representing the three switches on the breadboard. We then write out the wanted results, and this helps us derive the logic expression.
This particular table is different than the standard truth table as it has the a-g extension on the right side. This represents each of the segments in the display. If you read this a-g section horizontally it gives the segments that need to be on or off (1 being on and 0 being off) to create the wanted number for the input. The x that is put in as the output of the last two rows is to show that it doesn't matter what those two results will be as, all of the numbers have already been created. To get the logic expressions for each segment, on would have to read the a-g section vertically with each letter being its own mini-circuit that when all combined will create one large circuit.
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K-Mapping
These are the k maps for each of the segments with the logic expression for each.
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Karnaugh mapping or K-mapping is a very easy way to simplify logic equations without the use of Boolean Algebra, as it is much simpler with less rules and theorems to remember, which is why it is superior. The table for a three variable expression like this one is labeled as can be seen in the picture to right in order to encompass every possible combination of the variables. Then the outputs desired, in this case the vertical rows on the right extension of the table are put into the table in the order of 1 2 3 4 7 8 5 6. For example for the segment A the first result would be 0 and the rest would follow like so,1 1 1 X X 1 1. In this case the X can be used to represent either a 1 or a 0, whichever is more convenient. After the 1s and 0s are put into the table, the next step would be to group the 1s in the biggest possible groups, while including all of them. The only groups that can be used however are 2x2, 2x4, 1x2, 1x1, and 1x4. Although these groups can wrap around to the opposite ends of the table i.e. top row to bottom and left column to right. Finally you would use the groups to find the expression for that group. Any variable that changes from regular to inverse in a group is eliminated, leaving just the variables that need to inverted or regular. The expressions we get are in sum of product form, and we get so many because we need one for each segment at most, which means we need 7 at most. I say at most because some people got lucky, and some of there numbers were repeated, meaning they could just put the same wire to the two different segments.
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Multisim replication
This is the multisim implication of the circuit that I would later wire.
This circuit is in bus form. That means that the possible inputs are connected on the left and on the right each gate can be connected to the needed input by drawing a wire to the bus (the vertical thick line) and specifying which input is needed. The circuit requires 5 AND gates, 5 OR gates, 3 inverters, and 4 NOR gates. Since 4 gates fit into one chip, I would need 2 AND chips, 2 OR chips, 1 inverter chip, and 1 NOR chip.
I chose the A gate to be created using only NOR gates because it only used OR gates in the first place, and it is much easier to replicate the OR with a NOR gate than a NAND gate. We use NAND and NOR gates to simplify circuits that would otherwise use large amounts of chips and gates, as NORs and NANDs can be used to replicate all of the AOI gates. This is quite important as it would save money when building these circuits. In this particular situation changing he circuit to NOR did not make it simpler, in fact it added a gate. This is probably because it wasn't an extremely complected circuit to begin with, none of mine really were. Although it didn't really affect the final circuit that much because I still only needed one chip to complete it.
The seven segment display works by having a separate circuit for each segment. Depending on how these segments light up, different numbers will be shown on the display. A common cathode display like the one we used will have a segment light up if it gets a high or 1 input, it also needs to be connected to a ground source in order to work. An anode on the other hand lights up when it get s a low or 0 input, it must be connected to a voltage source in order to work. We used the common cathode because we have been taught that a high input makes a circuit work for the most part, so it would be much easier for us to create the logic expressions, rather than looking for the low inputs that work. The purpose of the resistors before the seven segment display is to make sure that the display doesn't get too much current and/or voltage, because if it did it would fry.
Bill of materials
This Bill of Materials shows what is needed o build the simplified circuit in its physical form i.e. a breadboard, chips, and wires.
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Breadbording
The wiring of the breadboard was quite easy, although it was a bit stressful, especially when the wires started getting very cluttered. However a lot of the pain was eased as I used the strategy of color-coding, to make my life easier in case I had to troubleshoot. I did eventually have to troubleshoot because the circuit did not function as designed at first. After extensively looking over the wires, I could not find the problem; so I decided to switch out the chip that all of the segments not working correctly went through. it turned out that out of all of the LS32 chips in the little bucket I was able to find one that didn't work. Which is the second wiring project in a row now where one of my chips was faulty.
Conclusion
In this project I learned how to create a circuit for a seven segment display, and also the importance of color-coding the wires, as that makes it much easier to troubleshoot if your circuit doesn’t work. I also learned that not every chip in the little buckets work, so next time I’ll be sure to check to make sure all of my chips work before I start tearing wires out and starting over (thankfully I didn’t do that this time). At the moment I have no questions regarding the material that we had to be able to use to be successful in this project. We also learned the importance of K-mapping, as in this instance with multiple mini-circuits in one big circuits, it would be a lot easier to just do a k-map for each rather than doing 7 sets of Boolean algebra simplification with 6 different midterms each.