MATH18584 Fundamentals of Computer Mathematics
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Assignment #2
This assignment will be graded out of 35
This assignment is to be completed individually. Assignments copied in whole or in part will
receive a grade of ZER0.
You must show your work for full marks!
Due Date: As per SLATE calendar.
Answers may only be submitted in the following formats:
o Microsoft Word Document (.docx)
o Adobe PDF Document (.pdf)
o Do not submit external links.
o Do not submit .zip files.
o Scanned documents need to be legible and in pdf format.
1. Find the output for each of the following combinatorial circuits: (2 x 2 marks)
a.
b.
2. Construct a circuit using only inverters, AND gates, and OR gates to produce these
outputs. Hint: start by creating the sum-of-products expression. Show all yours steps.
(5 marks)
�������������������
(𝑥𝑥̅ ⊕ 𝑧𝑧)(𝑥𝑥̅ + 𝑧𝑧)
3. Construct a k-map and simplify the following expression to its minimal form: (4 marks)
� + 𝐴𝐴̅𝐵𝐵� 𝐶𝐶̅ 𝐷𝐷 + 𝐴𝐴̅𝐵𝐵� 𝐶𝐶𝐶𝐶 + 𝐴𝐴̅𝐵𝐵 𝐶𝐶̅ 𝐷𝐷
� + 𝐴𝐴̅𝐵𝐵 𝐶𝐶̅ 𝐷𝐷 + 𝐴𝐴̅𝐵𝐵𝐵𝐵𝐵𝐵 + 𝐴𝐴𝐴𝐴𝐶𝐶̅ 𝐷𝐷
� + 𝐴𝐴𝐴𝐴𝐶𝐶̅ 𝐷𝐷 + 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
𝐴𝐴̅𝐵𝐵� 𝐶𝐶̅ 𝐷𝐷
4. List the members of the following sets: (2 x 1 mark)
a. (𝑥𝑥|𝑥𝑥 𝜖𝜖 𝑍𝑍 + , 𝑥𝑥 < 12} (Hint: 0 is considered a positive integer)
b. {x | x is the square of a whole number and x < 100}
5. Let U = {0,1,2,3,4,5,6,7,8,9,10}, A = {0, 2, 4, 6, 8, 10}, B= {0, 1, 2, 3, 4, 5, 6} and C = {4,
5, 6, 7, 8, 9, 10}
Evaluate and show all your work. ( 3 x 2 marks)
a. �����������
(𝐴𝐴 ∪ 𝐵𝐵)
b. 𝐴𝐴 ∩ 𝐵𝐵 ∪ 𝐶𝐶̅
c. 𝐴𝐴 − 𝐶𝐶
6.
100 visitors to Bitesize Festival completed a questionnaire
• All 100 visitors had seen at least one of the following bands – Band X, Band Y and
Band Z
• 14 of the visitors had seen Band X and Band Y and, of these, 4 had seen all bands
• 38 people had seen Band X
• 53 people had seen Band Y
• 55 people had seen Band Z
Some further information is given on the Venn diagram below
How many visitors had seen Band X but not Band Y or Band Z? Show all your steps. (4 marks)
7. Find the domain and range for the following, where y is a function of x:
(3 x 2 marks)
2
a)
𝑦𝑦 =
b)
𝑦𝑦 =
c)
𝑦𝑦 = 𝑥𝑥 2 − 2𝑥𝑥 + 5
√2𝑥𝑥−5
1
1
1−(𝑥𝑥−2)
8. The Ace Telephone Co. charges a flat monthly fee of $25.00 for a telephone line and
$0.20 per minute for long distance calls.
a. Write an equation that will relate the total cost per month, C, to the number of
minutes, m, of long distance calls that you make. (1 mark)
b. If you make 25 minutes of long distance calls per month, what will it cost? (1
mark)
9. Diane knows a phone call to a friend costs 25 cents for the first 3 minutes and 10 cents
for each additional minute. The number of minutes (m) you call and the cost (C) of the
call are related. Express the following relation as a function. (2 marks)