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CM-0107L Computer Architecture and Systems Software

Coursework 1

Semester 1, AY 2014/2015

Due date: December 5, 2014

Instructions:

It is a requirement to submit this coursework as electronic submission via Black-

board. Only word and pdf files are accepted. Please name your file as

CASS CW1 YourUoBnumber.doc or CASS CW1 YourUoBnumber.pdf

This document consists of two questions and one appendix in four pages. All ques-

tions and sub-questions are compulsory.

Total marks from all questions are 100 marks. Marks for each sub-question are indi-

cated in the corresponding sub-question. Marking criteria are indicated in Appendix

on page 6.

This coursework is worth 20% of the years assessment.

Submission deadline: The assignment must be submitted to the BlackBoard (under

Assessment) before 5pm on the 5th of December 2014. Do not forget to press the

SUBMIT button.

Feedback report on your coursework will be available in the BlackBoard at the

beginning of Semester 2.

CM-0107L page 1 of 6


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Suppose that the University of Bradford (UoB) wants to implement a new UoB identity

number for students. For the new number, the system will first reverse the current UoB

number and then insert a digit 9 at the beginning of the reversed number. Denote the

current UoB number as Hand the new UoB number as K.

Example:

If your current UoB number is

H= 12345678,

then your new UoB number will be

K= 987654321.

If your current UoB number is

H= 14027212

the your new UoB number will be

K= 921272041

Question 1: Number Systems and Representation

A. Among the bases from 2, 3, . . . ,to 10, which of those bases are possibly used in yourcurrent UoB number (H)? Will your answer change for your new UoB number (K)?

Justify your answers.

(Hint: The possible bases can be more than one option) [6 marks]

B. Assume that your new UoB number (K) is known to be in base 10. Suppose

that decimal number Mis obtained by dividing Kby decimal number 5000, i.e.,

M= K 5000

Mcan be represented as Mi Mj where the dot () indicates the decimal point.

B1. Derive the values ofMi and Mj. By treating each digit separately, evaluate

the ASCII representation of the first two letters ofMi and the last two letters

ofMj.

(Hint: ASCII code can be found in the lecture notes.) [8 marks]

B2. By showing relevant steps, translateMto octal number (i.e., base 8 number

system).

(Hint: You can limit the number of octal digits for the fraction up to maximum

6 digits.) [5 marks]

B3. By showing relevant steps, convert Mi to binary number (i.e., base 2 number

system). [5 marks]



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B4. By showing relevant steps, convert Mto binary number (i.e., base 2 number

system).

(Hint: You can limit the number of binary digits for the fraction up to maxi-

mum 6 digits.) [5 marks]

B5. Evaluate the sign-magnitude representation ofMi in a 20-bit length.[5 marks]

C. Consider base 20 number system where the symbols are given by:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J

Those symbols are equivalent to decimal numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Example:

A20= 1010

J20 = 1910

Assume that your new UoB number (K) is known to be in base 20 number

system.

C1. A base-20 number Nis obtained by dividing Kwith 5000 (in base 20), i.e.,

(N)20= (K)20 (5000)20

Evaluate the value ofN.

(Hint: You can perform division in base 10 (by first converting the number to

base 10). But, you need to convert the division result back to base 20. You can

limit the number of base-20 digits for the fraction up to maximum 6 digits.)

[11 marks]C2. Following C1, by showing the necessary steps, convertNto the corresponding

decimal number (base 10) and hexadecimal number (base 16).

(Hint: You can limit the number of hexadecimal digits for the fraction up to

maximum 6 digits.) [7 marks]

C3. Suppose Ni is the integer part ofN. Evaluate the representation ofNi in a

24-bit length string using twos complement method. [7 marks]

C4. Continuing from C3, suppose thatL is a base-20 number obtained from the

last two letters ofNi. Evaluate (L)20+(281)10using 24-bit twos complement

arithmetic. [11 marks]



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of bit position, i.e.,

(X,Y,Z) = (0, 0, 0) then A= b0

(X,Y,Z) = (0, 0, 1) then A= b1

(X,Y,Z) = (0, 1, 0) then A= b2...

...

(X,Y,Z) = (1, 1, 1) then A= b7.

A. Evaluate and show the truth table for functionGfrom all combination of inputs.

[9 marks]

B. Determine the standard forms of the Boolean expressions:

B1. Using a sum of products expression; [5 marks]

B2. Using a product of sums expression. [5 marks]

C. Simplify the Boolean expression in B1 (sum of products) using algebraic manipula-

tions.

[11 marks]



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Appendix

Marking schemes and criteria in terms of percentage of the marks:

0-20 % Basic and confused understanding with erroneous calculations and program-

ming

20-40 % Basic understanding with some correct and some erroneous steps and cal-

culations

40-60 % Good understanding mostly correct steps and calculations but with minor

mistakes or missing point

60-80 % Good demonstration of understanding of with correct steps and calculations

but non-significant errors

80-100 % Outstanding demonstration of understanding of with correct steps and cal-culations with good presentation


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