Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.5 - Page 94: 22

Answer

$100000000_2$ $256_{10}$

Work Step by Step

1. See below for the addition, we get $11111111_2+1_2=100000000_2$ 2. convert the result to decimal notation: $100000000_2=(1\times2^8+0)_{10}=256_{10}$ 3. Thus verifying that $11111111_2=(2^8-1)_{10}=(256-1)_{10}=255_{10}$
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