base: Base b Representation of a Number

In EnvStats: Package for Environmental Statistics, Including US EPA Guidance

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 ([e-mail])

References

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

See Also

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 Sept. 11, 2024, 6:03 p.m.