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assignment 1 Unit 18: Discrete Maths, Essays (university) of Internet and Information Access

LO3: Investigate solutions to problem situations using the application of Boolean algebra LO4: Explore applicable concepts within abstract

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2023/2024

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Unit 18: Discrete Maths
Assignment Brief
Student Name/ID Number
Unit Number and Title
Unit 18: Discrete Maths
Academic Year
Unit Tutor
Assignment Title
Assignment 2
Issue Date
Submission Date
Submission Format
Format:
This assignment should be completed in teams of 3 or 4 students.
Your team is tasked with preparing a formal 15-minute presentation, using 10-12 slides as a
guide.
Submission:
Students are compulsory to submit the assignment on the due date and in a way requested
by the Tutor.
The form of submission will be a soft copy posted on https://cms.btec.edu.vn/
Remember to convert the file (normally Word) into a PDF file before the submission on
CMS.
Note:
The Assignment must be the result of your team effort and should not be copied from
another student, group, or any external source.
Ensure comprehension and adherence to guidelines to prevent from plagiarism. Non-compliance
will lead to Assignment failure.
Unit Learning Outcomes
LO3: Investigate solutions to problem situations using the application of Boolean algebra
LO4: Explore applicable concepts within abstract algebra
Transferable skills and competencies developed
pf3
pf4
pf5

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Unit 18: Discrete Maths

Assignment Brief

Student Name/ID Number Unit Number and Title Unit 18: Discrete Maths Academic Year Unit Tutor Assignment Title Assignment 2 Issue Date Submission Date Submission Format Format: ● This^ assignment^ should^ be^ completed^ in^ teams^ of^3 or^4 students.  Your team is tasked with preparing a formal 15-minute presentation, using 10 -12 slides as a guide. Submission: ● Students are compulsory to submit the assignment on the due date and in a way requested by the Tutor. ● The form of submission will be a soft copy posted on https://cms.btec.edu.vn/ ● Remember to convert the file (normally Word) into a PDF file before the submission on CMS. Note: ● The Assignment must be the result of your team effort and should not be copied from another student, group, or any external source. Ensure comprehension and adherence to guidelines to prevent from plagiarism. Non-compliance will lead to Assignment failure. Unit Learning Outcomes LO3 : Investigate solutions to problem situations using the application of Boolean algebra LO4 : Explore applicable concepts within abstract algebra Transferable skills and competencies developed

Vocational scenario

Activity 1

Part I. Discuss the utilization of Boolean Algebra in addressing binary problems encountered in

two diverse real-world domains and the practical applications therein.

Part II.

  1. Develop the truth table and derive the corresponding Boolean equation for each of the following scenarios. a) "In a secure facility, if the access card is swiped OR the correct PIN is entered AND the security system is NOT in maintenance mode, then the door should unlock." b) "For a computer to successfully log in, either a valid username and password combination must be entered OR a security token must be provided, but not both."
  2. Generate a truth table for the provided Boolean expression.

xyz  x y z  xy z  x yz.

Part III. Simplify the following Boolean expressions.

1. x x (  y )  y y (  z )  z z (  x ).

2. ( x  y )( y  z )  ( x  y )( z  x ).

3. ( x  y )( xz  xz )  zx  x.

4. x x (  y )  ( x  y )( x  y ).

Part IV. Build a circuit using OR gates, AND gates, and inverters that produces an output of 1 if a

decimal digit, encoded using a binary coded decimal expansion, is divisible by 3, and an output of 0 otherwise. Identify the representation of the Boolean function that has the output value.

Activity 2

Part I.

  1. Explain the attributes of various binary operations executed within a common set.
  2. Check whether the operations applied to pertinent sets qualify as binary operations. a) Subtraction on set of natural numbers.

( , x y )  x  y.

b) Exponential operation on set integers.

^ :    

y

x y  x

Assignment activity and guidance

Activity 1

In this activity, each group has to encompass the following contents:

  1. Present two main ideas related to representing numbers in binary and using logic gates.
  2. For each given scenario, break it down into its components, re-express it as a Boolean equation, and create the corresponding truth tables.
  3. Simplify the given Boolean expressions.
  4. Build a circuit using an OR gate, an AND gate, and an inverter that produces the required output.

Activity 2

In this activity, each group must cover the following contents:

  1. You should present the definition of a binary operation and its properties, including closure, associativity, commutativity, identity element, inverse element, distributivity, and idempotence. Then, apply these properties to assess whether the given sets qualify as binary operations.
  2. Explain the concept of the order of a group. Then, construct the operation tables for group G with orders 1, 2, 3, and 4, using the given elements.
  3. State Lagrange's theorem in group theory, and then apply it to a specific case.
  4. Check if the given set is a group under the binary operation.
  5. Show the formula for calculating the number of binary operations based on the order of a group and apply it to specific situations.
  6. Choose an appropriate topic related to the application of group theory in computer science to present within 15 minutes. Students should prepare 10-12 slides. Several suggested key topics: Error Detection and Correction, Cryptography, Computer Graphics and Animation, Database Query Optimization, Network Security, Machine Learning, Computer Algebra Systems, Algorithm Design,... Recommended Resources Please note that the resources listed are examples for you to use as a starting point in your research – the list is not definitive.

Learning Outcomes and Assessment Criteria

Pass Merit Distinction LO3 Investigate solutions to problem situations using the application of Boolean algebra P5 Diagram a binary problem in the application of Boolean algebra. P6 Produce a truth table and its corresponding Boolean equation from an applicable scenario. M3 Simplify a Boolean equation using algebraic methods. D3 Design a complex system using logic gates. D4 Explore, with the aid of a prepared presentation, the application of group theory relevant to your given example. LO4 Explore applicable concepts within abstract algebra P7 Describe the distinguishing characteristics of different binary operations that are performed on the same set. P8 Determine the order of a group and the order of a subgroup in given examples. M4 Validate whether a given set with a binary operation is indeed a group.