Thinking Mathematically (6th Edition)

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

Chapter 4 - Number Representation and Calculation - 4.2 Number Bases in Positional Systems - Exercise Set 4.2 - Page 227: 71


Say, a number\[n\] with \[d\] digits to the base 10. Desired base b, has place values. \[\ldots {{b}^{3}},{{b}^{2}},{{b}^{1}},{{b}^{0}}\] Find place values that are less than n. Divide ntill a reminder that’s not divisible by leftmost place-value, then divide the remainder by lower place-value. Rewriting n in terms of groups of base b place-values, \[{{n}_{b}}=\ldots \left( {{d}_{3}}\times {{b}^{2}} \right)+\left( {{d}_{2}}\times {{b}^{1}} \right)+\left( {{d}_{1}}\times {{b}^{0}} \right)\] The number n is converted to base b.
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