# Spring 2008 CDA5155 Homework 1

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Spring 2008

CDA5155

Homework
1

Date assigned: January
1
8, 2008

Due date: January 30, 2008 (11:59 pm)

Due date for UF EDGE: February 6, 2008 (11:59 pm)

Total Points: 100 pts

(Important: if the
exercise is from case studies of textbook, please read the case study
description carefully before solving problem)

Chapter 1

Exercise 1

(5/
10/5
pts
=20
pts)

Analyze the reliability of a multimedia system which has following
components

and
MTTF (mean time to

failure):

1 power supply, 100,000
-
hour MTTF

1 fan, 500,000
-
hour MTTF

5
GPUs (graphics processing unit)
,
each rated at
500,000
-
hour MTTF

2 SCSI controllers,
each rated at
100,000
-
hour MTTF

2

disks,
each rated at
2
,000,000
-
hour MTTF

1 displayer, 1,000,000
-
h
our MTTF

Assume the lifetimes of components are exponentially distributed and their failures are
independent.

a)

Compute the MTTF of the whole system.

b)

If we improve the reliability of
each GPU from 500,000
-
hour to 50,000,000
MTTF, what’s the reliability impro
vement of the whole system? You must
analyze this question with Amdahl’s Law.

c)

If you could only improve the reliability of one type of component by 5 times
from above 6 types, which type of component would benefit the reliability of the
whole system most?

Exercise 2 (
5/5/10
pts
=20
pts)

Solve Exercise 1.12 (a. b. d.) from the book (H & P, 4
th
Edition)

Exercise 3 (5/5/5
/5
pts=20
pts)

A certain machine with a 10ns c
lock period can perform jumps (
2

cycle), branches (3
cyc
les), arithmetic instructions (
1

cycles),
multiply instructions (5 cyc
les), and memory
instructions (
10

c
ycles). A certain program has
5
% jumps, 1
5
% branches, 50% arithmetic,
5
% multipl
y, and 2
5
% memory instructions. Answer the following questions. S
how your
derivation in sufficient
detail.

(1) Wh
at is the CPI if this program on this machine.

(2) If the program executes 10^9
instructions
, what is its execution time?

(3) A 5
-
cycle multiply
-
add instruction is implemented that combines an
arithmetic

and a
multiply instruction.
2
0% of the multiplies ca
n be turned into multiply
-
new CPI?

(4) Following (3) above, if the clock period remains the same, what is the program

s new
execution time?

Appendix B

Exercise 4 (5/5/5/5pts=20
pts
)

The value represented by the hexadecimal number
4350 414
F 4148
4
3
4
F

is to be stored
in an aligned 64
-
bit double word.

a. Using the physical arrangement of the first row in Figure B.5 (Page B
-
8
, H & P, 4
th
Edition
), write the value to be stored using Big Endian byte order. Next, interpret each
byte as an ASCII c
haracter and below each byte write the corresponding character,
forming the character string as it would be stored in Big Endian order.

b. Using the same physical arrangement as in part a), write the value to be stored using
Little Endian byte order and be
low each byte write the corresponding ASCII character.

c. What are the hexadecimal values of all misaligned 2
-
byte words that can be read from
the given 64
-
bit double word when stored in Big Endian byte order?

d. What are the hexadecimal values of all misa
ligned 4
-
byte words that can be read from
the given 64
-
bit double word when stored in Little Endian byte order?

Exercise 5 (10
/
5
/
5
pts=
20
pts
)

When designing memory systems it becomes useful to know the frequency of memory
reads versus writes and also acces
ses for instructions versus those for data.
Assume a

certain
program has
5
% jumps, 1
5
% branches, 50% arithmetic,
5
% multipl
y, and 2
0
%