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: 36

Answer

$29$

Work Step by Step

Step 1: $(123)_{10}=(64+32+16+8+2+1)_{10}$ $(123)_{10}=((1)2^6+(1)2^5+(1)2^4+(1)2^3+(0)2^2+(1)2^1+(1)2^0)_{10}$ $(123)_{10}=(1111011)_2$ Step 2: $(94)_{10}=(64+16+8+4+2)_{10}$ $(94)_{10}=((1)2^6+(0)2^5+(1)2^4+(1)2^3+(1)2^2+(1)2^1+(0)2^0)_{10}$ $(94)_{10}=(1011110)_2$ $(1011110)_2 \xrightarrow{flip} (0100001)_2 \xrightarrow{+1} (0100010)_2 = (-94)_{10}$ Step 3: $(1111011)_2 + (0100010)_2 = (0011101)_2$ Answer: $(0011101)_2 = (16+8+4+1)_{10} = (29)_{10}$
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