Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3 - Page 235: 54


Consider a, 8- base number system, where there are digits 0-7in the number system. Also, take the numbers such that the sum of the numbers is bigger than the base. \[\begin{align} & \text{ 1 1} \\ & \text{ }162 \\ & +537 \\ & \text{ }\begin{matrix} 721 \\ \end{matrix} \\ \end{align}\] For the above solution, first, add 7 and 2 \[\begin{align} & {{2}_{eight}}+{{7}_{eight}}=9 \\ & ={{11}_{eight}} \end{align}\] Now add, \[\begin{align} & 6+3+1={{10}_{eight}} \\ & ={{12}_{eight}} \end{align}\] And, \[5+1+1={{7}_{eight}}\] The numbers are added in the same way as in the ten base. When the sum of 2 numbers become equal to or larger than the given base, use the mental conversions to convert the numeral from the 10-base to the required base (base-8 in this case).
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