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: 33

Answer

-79 1011 0001

Work Step by Step

Since the two terms are negative you may treat them as positive while you add them and then take 2s compliment of the sum. convert to binary using continuous divide by two 6/2 = 3 R 0 Least significant 3/2 = 1 R 1 1/2 = 0 R 1 Most significant 6 = 0000 0110 73/2 = 36 R 1 Least significant 36/2 = 18 R 0 18/2 = 9 R 0 9/2 = 4 R 1 4/2 = 2 R 0 2/2 = 1 R 0 1/2 = 0 R 1 73 = 01001001 Add the two binary numbers together 0100 1001 + 0000 0110 = 0100 1111 Take 1s complement (invert each bit) 1011 0000 Take 2s complement (add 1) 1011 0001 convert back to decimal using place value -128 + 0 + 32 + 16 + 0 + 0 + 0 + 1 = -79
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