Radix ( $b$ )

The radix is the base of positional notation. In the ordinary integer-base case it is an integer

b \geq 2

, and successive place values differ by a factor of

b

.

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- Mixed radix Radix

Mixed radix ( $n = \sum_{i} x_{i} \prod_{j < i} b_{j}$ )

A positional representation in which each digit has its own positive integer base. Least-significant-first digits satisfy

0 \leq x_{i} < b_{i}

, and digit

i

\prod_{j < i} b_{j}

. For

k

positions, assume

0 \leq n < \prod_{i = 0}^{k - 1} b_{i}

. Repeated Euclidean division by the successive bases converts that integer to digits; a backwards version of Horner's method converts the digits back.

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Radix by

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"Radix" can refer to different concepts depending on the context in which it is used: 1. **Mathematics**: In mathematics, "radix" refers to the base of a number system. For instance, the decimal system (base 10) has a radix of 10, while binary (base 2) has a radix of 2. The radix indicates how many unique digits, including zero, are available to represent numbers.

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