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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

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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, ...

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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:

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(11)

Fib(12)

Fib(13)

Fib(14)

Fib(15)

Fib(16)

Fib(17)

Fib(18)

Fib(19)

Fib(20)

Fib(21)

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 etc. You need to write and run the program using MARIE simulator. Please include appropriate comments to make your code readable.[10 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 [5 marks].

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 5 2-address instructions and 45 1-address instructions. How many 0-address instructions still you can fit? Justify your answer.  [7 marks]

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. [8 marks]

 

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Solution preview

PRIGRAM:
ORG 0
INPUT /READ NUMBER OF TERMS TO PRINT FIBONACCI SERIES
STORE NUM /STORE INTO NUM VARIABLE
LOAD FIB1 /LOAD FIB1 VARIABLE VALUE INTO ACCUMULATOR

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