Posted: January 9th, 2023

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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 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, write a paper (3-4 pages including graphs and tables) that includes 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 at least five 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.

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.

Competencies MeasuredBy successfully completing this assignment, you will demonstrate your proficiency in the following course competencies and scoring guide criteria:

Competency 1: Describe how discrete math theories are used in the fields of business and information technology.Apply Boolean logic to basic computer circuits in an application problem.

Set up a circuit application problem using Boolean logic.

Competency 2: Apply the methodologies of discrete math.Define the methodologies in discrete math needed to complete a circuit application problem.

Competency 4: Apply discrete math methods and tools to solve problems encountered in a work setting.Apply Boolean formulas to solve application problems.

Explain how to use Boolean formulas to solve application problems.

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