· Complete the attached Number System Assignment using the docx file following the directions provided on the page.
· Follow instructions in the assignment; Showing your work is required to earn full credit. Work or thought process for your question answers must be provided.
· AAB – Number System Assignment Spring 2024.docx
· Must follow Rubric Checklist: AAB – Number Systems Fall 2024.pdf
Submission Upload Requirements
1. Number System Worksheet (.pdf or .docx format only)
2. Number System Worksheet Additional Information (.pdf or .docx format only)
GaVS Number System Assignment – Abstraction and Algorithm Basics Module
Complete each of the following items showing your work or answer with justification (explain why your answer should be correct).
Work may be completed by hand and then saved and uploaded as discussed in the rubric.
Convert the given Decimal number to its Binary number. Note the subscript of base 10 which we do not normally write is used when and equal sign is used to show a number in the equivalent system. A binary number would be written on the other side of the equal with a base subscript of 2.
Example: 910 = 10012
A table of work (would be shown) as large for each number 1 – 4. Example below.
|
Binary |
23 |
22 |
21 |
20 |
|
8 |
4 |
2 |
1 |
|
|
910 = |
1 |
0 |
0 |
1 |
Convert the given Decimal number to its Binary number.
1. 2010 = ___________2
2. 8310 = ___________2
3. 21710 = ___________2
4. 15410 = ________2
5. Provide the process of the above conversion in 3 steps (abstractions – one for each row). The first abstracted step is given with the name I called the abstraction (the method – synonym for procedure or function) to accomplish the task. My example for 1 below calls the method setupBase. The method setupBase has two parameters, base and highExp. The purpose of the setupBase method: to setup the first row of the tables (the example and 1 – 4 above) using two parameters, the base value and highExp value passed into the method. I would pass in the first parameter as 2 for the conversion base and the second parameter as 3 for the highest exponent. You will not have to pass any parameters for your second and third row abstractions (methods).
You will need two create a method name for what happens in the second row and another method name for what happens in the third row of the table. Neither of these methods will need parameters. The name should give a hint of the methods’ purpose.
1. Method name: setupBase (base, highExp)
Purpose: Layout the base table first row base^highExp to base^0
2. Method name:
Purpose:
3. Method name:
Purpose:
Convert the given Binary number to its Decimal number.
Example: 1012
|
Binary |
23 |
22 |
21 |
20 |
|
8 |
4 |
2 |
1 |
|
|
0 |
1 |
0 |
1 |
8 * 0 + 4 * 1 + 2 * 0 + 1 * 1
= 0 + 4 + 0 + 1
= 510
6. 10102 = ________10
7. 10001112 = ________10
8. 01102 = ________10
9. 111001102 = ________10
10. What are the exact numbers and or letters that are used to represent values in each of the following bases? Work is not required for problem, only the answers.
|
Base |
Numbers and / or letters used in this base |
|
Binary – Base 2 |
|
|
Octal – Base 8 |
|
|
Hexadecimal – Base 16 |
|
|
Quinary – Base 5 |
|
|
Septinary – Base 7 |
11. Create the table for the use of Base 3 and show how the answer for the number below the chart is calculated using the chart to show work. Use the example chart for base 2 (binary) as a sample of what needs to be included in the chart below.
What is the number 1110 is in base 3?
|
Base 3 |
||||
1110 = _____________3
12. Name two numbers which are the same in all bases and explain why.
a. Numbers that are the same in all bases are _________ and _________.
b. Why are these numbers the same in all number bases?
GaVS Spring 2024 1/19/24
1
,
# Rubric Yes / No
AAB Module – Number System Assignment
W – Worksheet WA – Worksheet Additional Information
1
W: One or two pdfs for your work. (a) Worksheet with some answers
named NumberSystem_W.pdf . W indicates the Worksheet itself. (b) An
additional pdf, as needed, for any problem answers that need a larger
area to write the answers named, NumberSystem_WA.pdf. "WA"
indicates the worksheet additional document. (a) Answers written neatly
by hand on either document is acceptable. (b) Written work must be
readable, meaning large enough and dark enough to read all of the parts.
(c) Margins must be respected and work should not be cut off by a scan
or image taken when converted to a pdf.
2 Final Answers to math work required problems are circled or squared in
1 – 4 and 6 – 9.
3
All answers are neat and easily readable. Problems are done, provided in
order, with the exception if some are on the original document and work
is on separate paper (mark the original document with "see work paper").
Work paper items should be in numerical order.
4
Problem 1 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
5
Problem 2 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
6
Problem 3 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
7
Problem 4 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
8 Problem 5 answered with definition of what is to happen in the
abstraction and your name for the abstraction for both part 2 and part 3.
GaVS Spring 2024 1 of 1 7/4/2024
# Rubric Yes / No
AAB Module – Number System Assignment
9
Problem 6 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
10
Problem 7 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
11
Problem 8 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
12
Problem 9 demonstrates work for the answer and provides the answer.
Incorrect work and the correct answer or no work and the correct answer
will only receive 1 point towards the total points for the problem.
13 Problem 10 answer all parts with work as necessary.
14 Problem 11 demonstrates work for the answers placed in the table.
Correct answers with no work will not receive full credit.
15 Problem 12 identifies the numbers and explains why.
GaVS Spring 2024 2 of 2 7/4/2024
