Assignment
Task
1. (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:
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Fib(0)
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Fib(1)
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Fib(2)
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Fib(3)
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Fib(4)
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Fib(5)
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Fib(6)
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Fib(7)
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Fib(8)
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Fib(9)
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Fib(10)
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0
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1
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1
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2
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3
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5
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8
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13
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21
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34
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55
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Fib(11)
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Fib(12)
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Fib(13)
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Fib(14)
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Fib(15)
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Fib(16)
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Fib(17)
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Fib(18)
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Fib(19)
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Fib(20)
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Fib(21)
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89
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144
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233
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377
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610
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987
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1597
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2584
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4181
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6765
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10946
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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 etc. You need to write and run the program using MARIE simulator. Please include appropriate comments to make your code readable.
(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.
2. You are designing an instruction set for your computer. All the instructions are of same size (11 bits long). The size of an address field is 4 bits. You have already designed six 2-address instructions and 30 1-address instructions. How many 0-address instructions still you can fit? Justify your answer.
3. Write codes to implement the expression: A= (B + C) * (D - E) on 3-, 2-, 1- and 0-address machines. In accordance with programming language practice, computing the expression should not change the values of its operands.
Rationale
This assessment task covers topics on CPU operation and Instruction Set Architecture, and has been designed to ensure that you are engaging with the subject content on a regular basis. More specifically it seeks to assess your ability to:
• be able to investigate the internal operation of the Central Processing Unit (CPU) and describe how it is used to execute instructions;
• be able to investigate and describe in detail the essential elements of computer organisation including internal bus, memory, Input/Output ( I/O) organisations and interfacing standards and discuss how these elements function;