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

Published by Pearson Higher Education

# Chapter 1 - Data Storage - Section 1.7 - Storing Fractions - Questions & Exercises - Page 69: 4

#### Answer

The largest value would be $(7\frac{1}{2})$, which is represented by pattern $01111111$. The smallest positive value; you could argue that there are two “correct” answers. $First$, if you stick to the coding process described in the text, which requires the most significant bit of the mantissa to be $1$ (called normalized form), the answer is $(\frac{1}{32})$, which is represented by the pattern $00001000$. $The\ Second$ most machines do not impose this restriction for values close to $0$. For such a machine, the correct answer is $(\frac{1}{256})$ represented by $00000001$.

#### Work Step by Step

The largest value would be $(7\frac{1}{2})$, which is represented by pattern $01111111$. The smallest positive value, you could argue that there are two “correct” answers. $First$, if you stick to the coding process described in the text, which requires the most significant bit of the mantissa to be $1$ (called normalized form), the answer is $(\frac{1}{32})$, which is represented by the pattern $00001000$. $The\ Second$ most machines do not impose this restriction for values close to $0$. For such a machine, the correct answer is $(\frac{1}{256})$ represented by $00000001$

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