# base: Base b Representation of a Number In EnvStats: Package for Environmental Statistics, Including US EPA Guidance

 base R Documentation

## Base `b` Representation of a Number

### Description

For any number represented in base 10, compute the representation in any user-specified base.

### Usage

``````  base(n, base = 10, num.digits = max(0, floor(log(n, base))) + 1)
``````

### Arguments

 `n` a non-negative integer (base 10). `base` a positive integer greater than 1 indicating what base to represent `n` in. `num.digits` a positive integer indicating how many digits to use to represent `n` in base `base`. By default, `num.digits` is equal to just the number of required digits (i.e., `max(0, floor(log(n, base))) + 1)`. Setting `num.digits` to a larger number than this will result in 0's padding the left.

### Details

If `b` is a positive integer greater than 1, and `n` is a positive integer, then `n` can be expressed uniquely in the form

`n = a_kb^k + a_{k-1}b^{k-1} + \ldots + a_1b + a0`

where `k` is a non-negative integer, the coefficients `a_0, a_1, \ldots, a_k` are non-negative integers less than `b`, and `a_k > 0` (Rosen, 1988, p.105). The function `base` computes the coefficients `a_0, a_1, \ldots, a_k`.

### Value

A numeric vector of length `num.digits` showing the representation of `n` in base `base`.

### Note

The function `base` is included in EnvStats because it is called by the function
`oneSamplePermutationTest`.

### Author(s)

Steven P. Millard (EnvStats@ProbStatInfo.com)

### References

Rosen, K.H. (1988). Discrete Mathematics and Its Applications. Random House, New York, pp.105-107.

`oneSamplePermutationTest`.

### Examples

``````  # Compute the value of 7 in base 2.

base(7, 2)
#[1] 1 1 1

base(7, 2, num.digits=5)
#[1] 0 0 1 1 1
``````

EnvStats documentation built on Aug. 22, 2023, 5:09 p.m.