(a) Verify that a number in base b can be converted to

Chapter 1, Problem 1.24

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(a) Verify that a number in base b can be converted to base \(b^3\) by partitioning the digits of the base b number into groups of three consecutive digits starting at the radix point and proceeding both left and right and converting each group into a base \(b^3\) digit. (Hint: Represent the base b number using the power series expansion.)

(b) Verify that a number in base \(b^3\) can be converted to base b by expanding each digit of the base \(b^3\) number into three consecutive digits starting at the radix point and proceeding both left and right.

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