06 Feb Section 6.1, pages 264–265, problems

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.

MAT2051 Discrete Mathematics

Unit 2 Assignment

Graded Problem Set

Complete the following problems from your text. These problems are chosen to parallel the problems in The Practice Problem Sets study for this unit, so it is recommended to do those first, then post and discuss in the Practice Problem Set Review discussion so you are better prepared for this assignment.

Section 3.1, pages 125–126, problems 21, 63.

Section 3.2, pages 137–140, problems 27, 148.

Section 3.3, page 150, problem 31.

Section 3.4, page 156, problems 2, 12.

Section 3.5, pages 163–164, problems 3, 10.

Section 3.6, page 169, problem 12.

MAT2051 Discrete Mathematics

Unit 3 Assignment 1

Graded Problem Set

Complete the following problems from your text. These problems are chosen to parallel the problems in The Practice Problem Sets study for this unit, so it is recommended to do those first, then post and discuss in the Practice Problem Set Review discussion so you are better prepared for this assignment.

Section 6.1, pages 264–265, problems 2, 38.

Section 6.2, page 278, problems 12, 40.

Section 6.3, page 288, problem 2.

Section 6.5, page 299, problems 2, 6, 16, 21.

Section 6.6, pages 311–312, problems 2, 15, 29, 58.