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 - Chapter Review Problems - Page 88: 44

Answer

e. \( \frac{15}{16} \)

Work Step by Step

This value, \( \frac{15}{16}\), cannot be represented accurately in the given floating-point format because it involves a fraction that does not have an exact binary representation. This means that when converted into binary for storage in the floating-point format, it will likely be approximated, leading to potential loss of precision. 15/16 = 0.9375 To represent this, we’d need a significand of 1.111 and exponent of -1. But with only 4 bits of mantissa, we can't encode exactly 0.9375 in normalized form
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