Computer Science: An Overview: Global Edition (12th Edition)

Published by Pearson Higher Education
ISBN 10: 1292061162
ISBN 13: 978-1-29206-116-0

Chapter 1 - Data Storage - Section 1.7 - Storing Fractions - Questions & Exercises - Page 69: 3

Answer

$01001001$ $(\frac{9}{16})$ is larger than $00111101$ $(\frac{13}{32})$.

Work Step by Step

$01001001$ $(\frac{9}{16})$ is larger than $00111101$ $(\frac{13}{32})$. The following is a simple way of determining which of two patterns represents the larger value: $Case\ 1$. If the sign bits are different, the larger is the one with 0 sign bit. $Case\ 2$. If the sign bits are both $(0)$, scan the remaining portions of the patterns from left to right until a bit position is found where the two patterns differ. The pattern containing the $(1)$ in this position represents the larger value. $Case\ 3$. If the sign bits are both $(1)$, scan the remaining portions of the patterns from left to right until a bit position is found where the two patterns differ. The pattern containing the $(0)$ in this position represents the larger value. The simplicity of this comparison process is one of the reasons for representing the exponent in floating-point systems with an excess notation rather than with two’s complement. -- also, see image below:
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