**DATE OF BIRTH**

This project required us to create a circuit that displayed our date of birth on a seven segment display. We began using a truth table, then created a logic expression, eventually making the real circuit on Multisim and with a breadboard. We were required to use 220 ohm resistors and a common cathode display.

## Truth Table

This truth table was used to determine which segments were lit for each input, resulting in a distinct number each time. Truth tables are important because a logic expression and circuit can be easily made using them.

The X,Y, and Z columns represent which inputs are "on." The "display" column represents what number should result from the input combination. The a-g columns represent which segments need to be on to for the desired number. Each segment is assigned a specific letter

*a* being the top most segment in a figure 8 and*g*being the middle segment in a figure 8.*X*is used in the truth table because it does not matter what is indicated on the seven segment display for the last two inputs. An*x*is put into place to make K-mapping simpler.## Karnaugh maps and Simplified Logic

K- mapping is used to simplify truth tables into logic expressions through grouping. Groups are found by combining the 1's next to each other in groups of base 2. Groups can be found directly next to each other or can be found using a "pac-man" method of going across the barrier. Similarities in the groups are used to make the minterms in a sum-of-products form. K-mapping is easier than Boolean Algebra because it is quicker and requires almost no memorization of laws. X's are useful in K-mapping because they can be counted as a 1 of a 0, depending on which makes the simplest expression. There are many different expressions because one is needed for each segment (a-g).

## MultiSim Implementation

Below is a schematic for a circuit used to produce my date of birth using different input combinations.

This circuit was made using a bus to better organize the wires of my circuit. Producing the circuit to match the schematic would require 11 gates and 5 chips (1 invertor, 1 AND, 1 Or, 1 NAND, and 1 NOR. I chose to use NAND gates for segment A and a NOR gate for segment D because each one simplified to only using one gate each, instead of the 3 gates required when using AOI. We use NAND and NOR gates to reduce the number of chips, and maybe gates, required to produce a circuit. NAND and NOR gates can often make a circuit more efficient than if AOI gates were used.

Seven segment displays are either common cathode or common anode. Common cathode displays are connected to GND, so if they receive a high input the segment will be lit. If the display receives an off input the segment will not be lit. Common anode displays are connected to power, so if they receive a high input the segment will not be lit, but if it receives an off input the segment will be lit. The connection must be completed for any LED to work.

Seven segment displays are either common cathode or common anode. Common cathode displays are connected to GND, so if they receive a high input the segment will be lit. If the display receives an off input the segment will not be lit. Common anode displays are connected to power, so if they receive a high input the segment will not be lit, but if it receives an off input the segment will be lit. The connection must be completed for any LED to work.

## Bill of Materials

The bill of materials is a list of all the components needed to make my date of birth circuit.

*** breadboard includes seven segment display and resistors

## Breadboarding

My second experience breadboarding was better than my first. I had almost no issues, but the circuit did require more organization and focus. I only had issues remembering to connect my seven segment display to GND and bridging my breadboard. I did learn how to use NAND and NOR circuits on a breadboard. They work in reverse of the typical AOI chip, going right to left instead of left to right. The circuit was complex, but not too difficult.

## Conclusion

This project taught me the importance of organization when working with meticulous circuits and how to use NAND and NOR chips. I don't think I would change the way I did anything if I had to do it again, but I might plan on needed wire length better. K- mapping is useful because a complex truth table, such as the one we used, can be easily changed into a logic expression without the use of Boolean Algebra laws. Overall, I did enjoy this project and am beginning to find breadboarding more easy.