IT Fundamentals Assignment: Number Systems, MARIE Program, Memory

This assignment solution covers key concepts in IT Fundamentals, addressing number representation, MARIE assembly programming, and memory organization. Question 1 delves into IEEE-754 single-precision floating-point representation and base conversions between decimal, binary, octal, and hexadecimal systems. Question 2 presents a MARIE program designed to determine if a given integer is a prime number, including the program code and testing results. Question 3 explores memory interleaving techniques, including low-order and high-order interleaving, and examines memory organization with examples of address structures and module configurations for different interleaving approaches. The solution provides detailed explanations, step-by-step calculations, and clear code examples to facilitate understanding of these fundamental IT concepts.

Running head: IT FUNDAMENTALS
IT FUNDAMENTALS
Name of the Student
Name of the University
Author Note

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Question 1:
Q1.a
Sign Exponent Mantissa
0 01111110 10100000000000000000000
Sign bit = 0 (+ve)
Exponent – 01111110 = 2^(126-127)
Mantissa = 1 + 2^(-1)*1 + 2^(-2)*0 + 2^(-3)*1 + 0 = 1.625
Hence, decimal number – 1.625 *.5 = 0.8125
Q1.b
i)
AD9 in base 16 = 9*16^0 + D*16^1 + A*16^2 = 9 + 13*16 + 10*16^2 = 9 + 208 + 2560 =
2777. Hence, in base 3 = 2777 is divided by 3 in sequence.
Number Remainder after division by 3
2777 2
925 1
308 2
102 0
34 1
11 2
3 0
1 1
0
Hence writing remainders in reverse order gives 10210212 in base 3 (Xu, 2018).
ii)
451 in base 8
48=1002, 58 =1012 and 18=0012

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Hence, 451 in base 8 = 100101001 in base 2.
iii)
123.3 in base 5
= 1x5^2 + 2x5 + 3x5^0 + .3*5^(-1) = 25 + 10 + 3 + 0.6 = 38.6 in base 10
= Rem(6/8) Rem(38/8). Int(0.6*8) Int(0.8*8) Int(0.4*8)
= 46.463 in base 8
iv)
14.35 base 8
= 4*8^0 + 1*8^1 + 3*8^(-1) + 5*8^(-2)
= 12.453125 base 10
Question 2:
The Marie program to check whether a number is prime is shown below. It returns 1 if the
number is prime otherwise 0.
Marie code:
/ input number and store to variable a
Input
Store a
Load a / load number to accumulator
Subt b / subtract b starting from 2 from accumulator
Store t / store to t
Load b / load content of b to accumulator
Subt v / subtract content of v from accumulator
Store z / store result to z
/ main loop

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if1, Load z
Skipcond 000
Jump if
Jump loop2
if, Load t
Skipcond 000
Jump loop
Jump loop1
loop, Load x
Add v
Store x
Load p
Add b
Store p
Load t
Subt b
Store t
Skipcond 000
Jump loop
Load x
/ output 1 if prime otherwise 0
Load a
Subt p
Store y

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Output
Halt
loop1, Load x
Load a
Store y
Output
Halt
loop2,Halt
/ variable declaration
a, DEC 9
b, DEC 2
v, DEC 1
t, DEC 0
p, DEC 0
z, DEC 0
x, DEC 0
y, DEC 0
one, DEC 1
Testing:
Input number = 7
Output=1

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Input =17
Output = 1

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Input = 20
Output = 0

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Question 3:
a) Memory interleaving is used for increasing the throughput. The primary motive for
memory interleaving is to split the memory in two parts which are independent of each other
and can read and write data when requested by user. The two main formats of memory
interleaving is low order and high order interleaving. For the case of low order interleaving
the contiguous memory locations are horizontally divided through the modules. Thus, for
each of the module identification of memory module is performed by the low order bits and
for containing the addresses of word the high order bits are used (Antoniadis, Blanchard,
Guerraoui & Stainer, 2018). For the case of high order interleaving the module address is
contained for each module by high order bits and the address of word inside every module is
hold by the module’s low order bits.
b) Given the memory size is 32 4k X 8-bit chips.
i. High order interleaving address structure and module organization
Address Module
0-64M 0
64M-128M 1
128M-192M 2

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192M-256M 3
ii. Low order interleaving structure and module organization
Address Module
0 0
1 1
2 2
3 3
4 0
5 1
6 2
7 3
8 0
9 1

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References:
Antoniadis, K., Blanchard, P., Guerraoui, R., & Stainer, J. (2018). The entropy of a
distributed computation random number generation from memory interleaving. Distributed
Computing, 31(5), 389-417.
Xu, C. W. (2018). Animating Conversions Between Binary and Decimal. In Learning Java
with Games (pp. 511-534). Springer, Cham.