Essentials of Computer Organization and Architecture
Essentials of Computer Organization and Architecture
5th Edition
ISBN: 9781284123036
Author: Linda Null
Publisher: Jones & Bartlett Learning
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Chapter 11, Problem 4E

Explanation of Solution

Verification of the ratio being consistent when compared with the other system:

  • System performance is considered as one of main factor of a processor.
  • It is used to determine the speed a problem can be solved.
  • It is also used to determine the factors such as number of problems that can be allocated at particular amount of time and also the number of problems that can be handled by the processor.
  • The relative performance between the two systems is measured and expected by the run time of the program of the individual.

Given:

The information about the system A and System c are shown in the below table:

Program

Execution time

System A(sec)

Execution time

System B(sec)

Execution time

System C(sec)

V4512575
W300275350
X250100200
Y400300500
Z8001200700

Consider there are n programs and each programs are considered to have their own runtime on each systems.

Program

Execution time

System A(sec)

Execution time

System B(sec)

Execution time

System C(sec)

V4512575
W300275350
X250100200
Y400300500
Z8001200700

System A:

calculate the arithmetic mean for the system A:

A=(45+300+250+400+8005)=359

System B:

calculate the arithmetic mean for the system B:

A=(125+275+100+300+12005)=400

System C:

calculate the arithmetic mean for the system C:

A=(75+350+200+500+7005)=365

Calculating the ratio of the geometic mean obtained for the various systems are:

AM_AAM_B=359400=0.8975

AM_BAM_C=400365=1.095

AM_AAM_C=359365=0.983

Consider there are n programs and each programs are considered to have their own runtime on each systems.

The geometric mean of the one system’s runtime is obtained by normalizing it with the another system.

The process of normalization is carried out by taking the products of the ratio of the run time and by taking the nth root of the product.

The below tables illustrates the how the system B and system C is being normalized with that of the system A.

Program

Execution time

System A(sec)

Normalized to A

Execution time

System B(sec)

Normalized to B

Execution time

System C(sec)

Normalized  to C
V4511250.36750.6
W30012751.093500.857
X25011002.52001.25
Y40013001.335000.8
Z800112000.677001.14

Calculating geometic Mean:

The formula to calculate the geometric mean:

G=(x1×x2×x3×...×xn)1n

System A:

calculate the geometric mean for the system A:

G=(1×1×1×1×1)15=1

System B:

calculate the geometric mean for the system B:

G=(0.36×1.09×2.5×1.33×0.67)15=(0.874)15=0.973

System C:

calculate the geometric mean for the system C:

G=(0.6×0.857×1.25×0.8×1.14)15=(3.7042)15=1.299

Calculating the ratio of the geometic mean obtained for the various systems are:

GM_AGM_B=10.973=1.027

GM_BGM_C=0.9731.299=0.749

GM_AGM_C=11.299=0.769

From the comparison of the  arithmetic and geometric mean that is obtained with the every pair of system, the consistency is found only with the sytem A because the ratio of runtine in the system B and system C  is less than 1.

Likewise, The relative performance compariosn seems to be difficult to compared with that of the system A or B or with the system B or C.

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Chapter 11 Solutions

Essentials of Computer Organization and Architecture

Ch. 11 - Prob. 1RETCCh. 11 - Prob. 2RETCCh. 11 - Prob. 3RETCCh. 11 - Prob. 4RETCCh. 11 - Prob. 5RETCCh. 11 - Prob. 6RETCCh. 11 - Prob. 7RETCCh. 11 - Prob. 8RETCCh. 11 - Prob. 9RETCCh. 11 - Prob. 10RETC
Ch. 11 - Prob. 11RETCCh. 11 - Prob. 12RETCCh. 11 - Prob. 13RETCCh. 11 - Prob. 14RETCCh. 11 - Prob. 15RETCCh. 11 - Prob. 16RETCCh. 11 - Prob. 17RETCCh. 11 - Prob. 18RETCCh. 11 - Prob. 19RETCCh. 11 - Prob. 20RETCCh. 11 - Prob. 1ECh. 11 - Prob. 2ECh. 11 - Prob. 3ECh. 11 - Prob. 4ECh. 11 - Prob. 5ECh. 11 - Prob. 6ECh. 11 - Prob. 7ECh. 11 - Prob. 8ECh. 11 - Prob. 10ECh. 11 - Prob. 11ECh. 11 - Prob. 12ECh. 11 - Prob. 13ECh. 11 - Prob. 14ECh. 11 - Prob. 15ECh. 11 - Prob. 16ECh. 11 - Prob. 17ECh. 11 - Prob. 18ECh. 11 - Prob. 19ECh. 11 - Prob. 20ECh. 11 - Prob. 21ECh. 11 - Prob. 22ECh. 11 - Prob. 23ECh. 11 - Prob. 24ECh. 11 - Prob. 25ECh. 11 - Prob. 26E
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