Problem Statement / Constraints
To ensure accurate/secure voting we were asked to design and create two additional circuits using NAND and NOR logic to correspond with a version of our previous voting machine. The first is the BOOTH circuit which needs to turn on a light whenever at least 1 of 4 voting booths is open. The second is the ALARM circuit which needs to sound an alarm (in the form of an LED light) whenever two consecutive booths are occupied (i.e. A&B, B&C, or C&D).
What is NAND & NOR?
Alright so I have already talked about AOI gates i.e. AND, OR, INVERTER gates. Basically NAND and NOR gates are universal gates which means they are gates which can perform the functions of all of the AOI gates. This is important because it provides more options when designing circuits e.g. if AOI gates are expensive one could buy just NAND or NOR gates, which in the long run could save a lot of money, or if one type of circuit is simpler (uses less gates) than another one could save money that way.
NAND means NOT AND, and functions as the reverse of an AND gate (i.e. an AND gate and and INVERTER put together). NOR similarly means NOT OR, and functions as the reverse of an OR gate. See chart below.
As universal gates NAND and NOR gates arranged in different formations can perform as AND, OR, and INVERTERS. See chart below.
As you can see NAND and NOR gates like AND and OR gates are opposite in their functions. i.e. AND formation for NAND is OR formation for NOR, etc.
Brainstorming
Alright so first we were asked to design these circuits using AOI logic. The simplified midterm equations ....
BOOTH = A'B' + C'D' and ALARM = AB + BC + CD were provided and simplified using a process known as Karnaugh Mapping (K-Mapping).
*The K-Mapping Procedure consists of writing out all input combinations on the perimeter of a grid system and then filling in the true values. (Input combonations are organized by placing completely 'Not-ed' pairs in the upper left hand of the grid and then working outward.) After all true values have been entered they are grouped in order to be simplified, any input values that are repeated throughout a group are eliminated. For more on K-Mapping visit this link. Otherwise the below K-Maps and equations were provided.
BOOTH = A'B' + C'D' and ALARM = AB + BC + CD were provided and simplified using a process known as Karnaugh Mapping (K-Mapping).
*The K-Mapping Procedure consists of writing out all input combinations on the perimeter of a grid system and then filling in the true values. (Input combonations are organized by placing completely 'Not-ed' pairs in the upper left hand of the grid and then working outward.) After all true values have been entered they are grouped in order to be simplified, any input values that are repeated throughout a group are eliminated. For more on K-Mapping visit this link. Otherwise the below K-Maps and equations were provided.
Calculations and Design
Final Design
Reflection
I think that I have answered all of the questions on Edmodo other than why K-Mapping is better than Boolean Algebra. The advantages of K-mapping are that it is generally faster than using Boolean Algebra, it is difficult to mess up, and it appeals to visual learners. So unless you are gifted in math I would suggest using K-mapping. Other than that it was a fun project, and I now know how to use NAND and NOR logic which is surprisingly easier than using AOI.