Capella MAT2051 Unit 1 Assignment 2 Latest 2019 October

MAT2051 Discrete Mathematics

Unit 1 Assignment 2

Boolean Circuits
and Technology

This is the
first of five independent application assignments. Each assignment will allow
you to learn how the topics of this course apply to the areas of computer
science, Internet technology, or technology applications.

For this
assignment, imagine that we are many years into the future and you have been
hired by a technology company to create a human door key system. When a person
steps on a special mat containing sensors that is located at his or her front
door, these sensors grab information, send it through a set of circuits, and
reach a one of two logical conclusions:

Yes (or 1),
the person lives in this house and may enter.

No (or 0),
this person does not live in this house and may not enter.

If the
result is yes, the door automatically opens. If the result is no, you can
decide what happens.

For this
assignment, complete the following:

Define at
least five features that can be sensed by the magic door mat such that each
feature has a result of 0 or 1. This magical mat can sense anything, such as
weight, height, eye color, hair color, gender, and so on. Because the result of
the sensor can only be 0 or 1, you will have to think about how to do this. As
an example, if the weight is greater than 125, the sensor returns a 1, else a 0.
Similarly, if the hair color is NOT brown, the sensor returns a 0, else 1.
These are just some ideas.

Explain
each of your features clearly, including exactly what the 0 or 1 represents in
each case.

Using at
least five gates and at least five inputs, create a logical circuit that
describes your system. This circuit will have at least five inputs, at least
five gates, and one—and only one—output. Remember, the input values to and from
the gates are only 0 or 1, but you can name them according to what they represent.

Create a
logic table to show some examples of people who will and will not be able to
enter. This table will be labeled with your attributes and will contain values
of only 0 and 1.

Describe
your circuit using a Boolean expression with proper use of AND, OR, and NOT
symbols.

Describe
what will happen to a person who cannot enter (that is, when the output of the
circuit is 0). This is up to you, so feel free to be creative. Include at least
one paragraph explaining your circuit, your features, and what will happen in
cases where a person can or cannot enter the door. Hint: You can have the door
inform the person that they cannot enter and why.

You may
find it useful to read Chapter 11, pages 532–542, and look at the examples. You
can combine attributes to make sure only the right person gets in. For example,
if a person’s weight is greater than or equal to 125, you can have a 1. If the
weight is less than 125, you can have a 0. Therefore, if the person weighs 250
pounds, this would result in a 1. You can use the circuit creatively with AND,
OR, and NOT gates to grant or deny access using a set of measurable attributes.

Review the
Boolean Circuits and Technology Scoring Guide to understand how you will be
graded on this assignment.