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Computational Mathematics and Computer Architecture

Assessment Criteria – Computational Mathematics and Computer Architecture: Individual Assignment

ASSESSMENT SUMMARY

Question 1

1. Convert 1100 10012 to the following formats. Show your working clearly:

  1. Decimal
  2. Octal
  3. Hexadecimal

(6 marks)

2. Evaluate the following expressions. Show your working clearly:

  1. 11002 * 10112
  2. 7478 + 3508
  3. 0xACE + 0xCAFE

(6 marks)

3. Binary Converter Program - Write a program to accept a single binary number of up to 8 bits and display the equivalent in decimal.

(4 marks)

Question 2

1. Given the following matrices

-2 1              2              1              0              2

                                                 𝐴𝐴  =  (             ) , 𝐡𝐡  = (             ) , 𝐢𝐢   =  (                    )

-5 -2            7              -3            4              8

Evaluate the following, showing your steps clearly.

  1. A + B
  2. 3 (A – B)
  3. 2A * C
  4. Show that A * I = A where I is the identity matrix
  5. Prove that A * B is not equal to B * A

(12 marks)

2. Matrix Processing Program - Write a program to accept a 2 x 4 matrix from user input and find the following:

  1. Maximum element in the 2 x 4 matrix
  2. Minimum element in the 2 x 4 matrix
  3. Average of all elements in 2 x 4 matrix
  4. Sorted in a single array of elements

(8 marks)

Question 3

Given an expression

𝑋𝑋(𝑋𝑋 + π‘Œπ‘Œ) + (π‘Œπ‘Œ + 𝑋𝑋. 𝑋𝑋)(𝑋𝑋 + π‘Œπ‘Œ) + 𝑍𝑍 + 𝑋𝑋. 𝑍𝑍 

1. Draw the Boolean logic circuitry

(8 marks)

2. Construct the truth table for the above expression

(8 marks)

3. Simplify the Boolean expression.

(8. marks)

Question 4

Complete the following programs:

a. Driving Academy App - Write a program that ask for your age to determine the eligibility to learn theory or driving in the driving academy.

  1. If your age is below 18, output is “You can only learn theory from age 18 onwards”.
  2. If age is between 18 and 21, output is “You can only learn theory at this time”.
  3. If the age is above 21, output is “You can learn driving provided you have passed your theory."

(6 marks)

2. Children Incentive Program - Write a program to determine the incentive from government X depending on the person’s number of children.

  1. If the person has 1 child, bonus is $100.
  2. If the person has 2 children, bonus is $300.
  3. If the person has 3 or 4 children, the bonus is $500.
  4. If the person has more than 4 children, the bonus is $1000. Print the bonus the person should receive.

Request for input again until the user chooses to quit with a negative input for the children.

(6 marks)

3. Lucky Draw Game - Write a program that randomly generates a set of 7 winning numbers ranging from 1 to 30. The user will then be asked to key in 3 numbers.

  1. If all the 3 numbers are part of the winning numbers, display “Congratulations, you win!”
  2. If the entries are not part of 7 winning numbers, display the “missed” numbers. For example if the user keys in 1, 2, 3 and the winning numbers contain 1, 5, 6, 7, 8, 9, 10. The message displayed will be “Sorry, you missed on numbers: 2 3”
  3. If the user does not win the game, the game is restarted and a new set of random numbers is generated again.

(8 marks)

Question 5

Smart Plotter Program - Design an application that displays a menu to ask the user to choose whether to:

  1. Plot a graph from inputting values for both x and y axes or to
  2. Load a file to plot the graph.
  3. Quit the Smart Plotter

The user can choose then proceed to plot a simple 2D line, a scatter plot or a pie chart. The program will continue displaying the menu to allow the user to choose until the user chooses to quit the application.

(20 marks)

COMPUTATIONAL MATHEMATICS & COMPUTER ARCHITECTURE

Computational Mathematics and Computer Architecture

Total Marks

Marks awarded

Question 1 (a) ‐ Question 1 (b)

0 ‐ 4 marks

5 ‐ 8 marks

9 ‐ 12 marks

12

No working shown, Only answers shown.

Author does not detail the steps..

Steps for solving the problems are detailed but there are some problems or lack of detailed steps to the solution

Solution has detailed steps to reach the solution. Each step is necessary for the next step.

Question 1 (c)

0 ‐ 1 marks

2 ‐ 3 marks

4 marks

4

Able to read in values from user

Able to read bit values and convert into decimal values

Able to read bit values of the correct length and convert into appropriate decimal values.

Question 2(a)

0 ‐ 4 marks

5 ‐ 8 marks

9 ‐ 12 marks

12

No working shown, Only answers shown. Author does not detail the steps..

Steps for solving the problems are detailed but there are some problems or lack of detailed steps to the solution

Solution has detailed steps to reach the solution. Each step is necessary for the next step.

Question 2(b)

0 ‐ 3 marks

4 ‐ 6 marks

7 ‐  8 marks

8

Able to read in a 2 x 4 matrix and display its values and able to display the maximum, minimum element in each column

Able to read in a 2 x 4 matrix and display its values and able to display the maximum, minimum element, average of all elements for the entire matrix

Able to fulfill the requirements

Question 3(a)

0 ‐ 3 marks

4 ‐ 6 marks

7 ‐  8 marks

8

The Boolean Circuitry is drawn with correct number of gates and gate types but somewhat wrong inputs

The Boolean Circuitry is drawn with correct number of gates and gate types and correct inputs

The Boolean Circuitry is drawn with correct number of gates and gate types, correct inputs and intermediate steps with correct labeling to reach the solution

Question 3(b)

0 ‐ 3 marks

4 ‐ 6 marks

7 ‐  8 marks

8

No working shown, Only answers shown. Author does not detail the steps..

Steps for solving the problems are detailed but there are some problems or lack of detailed steps to the solution

Solution has detailed steps to reach the solution. Each step is necessary for the next step.

Question 3(c)

0 ‐ 3 marks

4 ‐ 6 marks

7 ‐  8 marks

8

No working shown, Only answers shown. Author does not detail the steps..

Steps for solving the problems are detailed but there are some problems or lack of detailed steps to the solution

Solution has detailed steps to reach the solution. Each step is necessary for the next step.

Question 4(a)

0 ‐ 2 marks

3 ‐ 4 marks

5 ‐ 6 marks

6

Able to read in values from user and display the values read

Able to read in values from user and display the values read and shows correct print out of the program

Able to read in desired values from the user, display the correct output with evidence of testing

0 ‐ 2 marks

3 ‐ 4 marks

5 ‐ 6 marks

Question 4(b)

Able to read in values from user and display the values read

Able to read in values from user and display the values read and shows correct print out of the program

Able to read in desired values from the user, display the correct output with evidence of testing

6

Question 4(c)

0 ‐ 3 marks

4 ‐ 6 marks

7 ‐ 8 marks

8

Able to read in values from user and display the values read

Able to read in values from user and display the values read and shows correct print out of the program

Able to read in desired values from the user, display the correct output with evidence of testing

Question 5

0 ‐ 8 marks

9 ‐ 16 marks

17 ‐ 20 marks

20

Able to read in values from user and display the values read

Able to read in values from user and display the values read, plot the selected charts properly and exit the loop correctly

Able to read in values from user or file correctly, save to files, plot the desired charts properly with correct labelling and exit the loop properly.

Formative comments on submission

     

100

WEIGHTAGE

      

80%
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