Invitation to Computer Science 8th Edition

Published by Cengage Learning
ISBN 10: 1337561916
ISBN 13: 978-1-33756-191-4

Chapter 4 - 4.2 - The Binary Numbering System - Practice Problems - Page 166: 10

Answer

You are adding the two values $+7$ and $+14,$ which should produce the value $ +21$. But when you add the two values together, you get 10101, which is a negative value because the leftmost digit is a $1 .$ In fact, it is the value $-5 .$ What happened is that we got an arithmetic overflow. The value $+21$ is too big to represent in sign/magnitude with only five digits.

Work Step by Step

You are adding the two values $+7$ and $+14,$ which should produce the value $ +21$. But when you add the two values together, you get 10101, which is a negative value because the leftmost digit is a $1 .$ In fact, it is the value $-5 .$ What happened is that we got an arithmetic overflow. The value $+21$ is too big to represent in sign/magnitude with only five digits.
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