Question 1.
a) Determine the value of base b if (152)b = 0x6A. Please show all steps. [3 marks]
b) Convert the followings: (Please show all steps; no marks will be awarded if no steps are shown) [1.5x4 = 6 marks]
i) 0xBAD into 3base representation
ii) 3217 into 2base (binary) representation
iii) 1235 into octal representation
iv) 21.218 into decimal representation
c) Given a (very) tiny computer that has a word size of 3 bits, what are the lowest value (negative number) and the highest value (positive number) that this computer can represent in each of the following representations? [3 marks]
i) One's complement
ii) Two's complement
iii) Signed Magnitude
Question 2.
a) The Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and are characterised by the fact that every number after the first two is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 114, … etc.
By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. We define Fib(0)=0, Fib(1)=1, Fib(2)=1, Fib(3)=2, Fib(4)=3, etc. The first 22 Fibonacci numbers given below:
Fib(0 
Fib(1 
Fib(2 

Fib(3 

Fib(4 

Fib(5 

Fib(6 

Fib(7 

Fib(8 

Fib(9 

Fib(10 
) 
) 
) 
) 
) 
) 
) 
) 
) 
) 
)  



















0 
1 
1 
2 
3 
5 
8 
13 
21 
34 
55  






































Fib(1 
Fib(1 
Fib(1 

Fib(1 

Fib(1 

Fib(1 

Fib(1 

Fib(1 

Fib(1 

Fib(2 

Fib(2 
1) 
2) 
3) 

4) 

5) 

6) 

7) 

8) 

9) 

0) 

1) 



















89 
144 
233 

377 

610 

987 

1597 

2584 

4181 

6765 

10946 



















Write a MARIE program to calculate Fib(n), where the user inputs n. For example, if the user inputs 7, the program outputs the value 13; if the user inputs 15, the program outputs the value 610; if the user inputs 20, the program outputs the value 6765 and so on. You need to write and run the program using MARIE simulator. Please include appropriate comments to make your code readable. [8 marks]
b) For some values of n, your program will not produce correct results. You can check this by gradually increasing the values of n and checking for the correct outputs. What is the maximum value of n for which your program produces a correct result? Why? Please comment on this [3 marks].
Question 3.
a) What are the 'interrupts' in a computer system? Describe the approaches to deal with multiple interrupts in a system. [4 marks]
b) Analyse the benefits of using a multiplebus architecture compared to a singlebus architecture for a computer system. [3 marks]