# baseconvert

Convert any rational number, from any (positive integer) base, to any (positive integer) base. Output numbers as tuple or string.

- Any rational number
- Arbitrary precision
- Fractions
- Recurring/repeating fractional digits.
- Input numbers as tuple or string or number.
- Output numbers as tuple or string.

MIT License (MIT) Copyright (c) 2016 Joshua Deakin

## Requires

- Python 3

## Install / Uninstall

Install:

```
pip install baseconvert
```

Uninstall:

```
pip uninstall baseconvert
```

## Quickstart

```
# base(number, input_base, output_base)
>>> base((15, 15, 0, ".", 8), 16, 10)
(4, 0, 8, 0, '.', 5)
>>> base("FF0.8", 16, 10, string=True)
'4080.5'
>>> base("4080.5", 10, 16, string=True)
'FF0.8'
```

Or from command line

```
$ echo 4080.5 | python -m baseconvert -i 10 -o 16
FF0.8
$ python -m baseconvert -n 4080.5 -i 10 -o 16
FF0.8
```

## Tuple representation

Numbers are represented as a sequence of digits. Each digit is a base-10 integer value. The radix point, which separates the integer and fractional parts, is denoted by a string period.

```
(int, int, int, ... , '.', ... , int, int, int)
( integer part , '.', fractional part )
```

## String representation

String digits (after z the values are in ascending Unicode):

```
0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
| Value | Representation |
|---------|----------------|
| 0 - 9 | 0 - 9 |
| 10 - 53 | A - Z |
| 36 - 61 | a - z |
| 62 + | unicode 123 + |
For bases higher than 61 it's recommended to use tuple representation.
```

## Examples

```
# base(number, input_base, output_base)
>>> n = (15,15,".",0,8)
>>> base(n, 16, 10)
(2, 5, 5, '.', 0, 3, 1, 2, 5)
>>> base(n, 16, 10, string=True)
'255.03125'
>>> base("FF.08", 16, 10) == base((15,15,".",0,8), 16, 10)
True
# A callable BaseConverter object can also be created.
# This is useful for when several numbers need to be converted.
>>> b = BaseConverter(input_base=16, output_base=8)
>>> b("FF")
(3, 7, 7)
>>> b((15, 15))
(3, 7, 7)
>>> b("FF") == b((15,15))
True
>>> base(0.1, 3, 10, string=True)
'0.[3]'
```

### Recurring digits

Recurring digits at the end of a fractional part will be enclosed by "[" and "]" in both string and tuple representation. This behavior can be turned off by setting the recurring argument of base or BaseConverter object to False.

```
>>> base("0.1", 3, 10, string=True)
'0.[3]'
>>> base("0.1", 3, 10, string=True, recurring=False)
'0.3333333333'
```

### Max fractional depth

Integer parts are always of arbitrary size. Fractional depth (number of digits) can must be specified by setting the max_depth argument of base or a BaseConverter object (default 10).

```
>>> base("0.2", 10, 8)
(0, '.', 1, 4, 6, 3, 1, 4, 6, 3, 1, 4)
>>> base("0.2", 10, 8, max_depth=1)
(0, '.', 1)
```