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Parse & write real numbers in any base, including balanced bases.

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# glathoud/numbase

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# numbase

`numbase` is a JavaScript implementation to encode and decode string representations of numbers in any base, including balanced bases:

``````<float value> <=> "<string representation>"
``````

Integer examples:

``````123 <=> "2:1111011" (binary)
123 <=> "b3:1_1_1_1_10" (balanced ternary)
``````

Real number examples:

``````-123.25 <=> "2:-1111011.01" (binary)
-123.25 <=> "b3:_111110_11_11_11_11_11_11_11_11_11_11_11_11_11_11:_100_1"
(balanced ternary, "_100_1" is the exponent)
``````

Inspiration: Third Base, a column from Brian Hayes published in the November-December 2001 issue of American Scientist.

## Explanations

For a complete article including more explanations and an interactive area, please open ./index.html (live version) with a browser.

## API Usage

Use the underscore `"_"` before a negative digit. For example, a balanced ternary number can be written in a text editor `"_101_1"` which corresponds to the decimal value:

``````-1*(3*3*3) + 0*(3*3) + 1*3 -1*1 = -25
``````
• `numbase.parseInt( <intString>, <base> )`

converts an integer of any base to a decimal value, for example:

``````var decimal_value = numbase.parseInt( "_101_1", "b3" );
// -25
``````
• `numbase.parse( <fullString> )`

converts a float of any base to a decimal value. `<fullString>` contains three parts, separated by column: (1) the base, (2) integer and/or fractional part(s) and (3) an optional exponent. For example the string:

``````"b3:_10.1_1"
``````

represents in balanced ternary base a float with decimal value:

``````-1*3 + 0*1 + 1/3 - 1/(3*3) = -2.7777777777777777
``````

Let us now append an exponent `110`:

``````"b3:_10.1_1:1_10"
``````

This has the effect of multiplying by the decimal value:

``````3^(1*(3*3) - 1*3 + 0) = 3^6 = 729
``````

so that we should obtain the decimal value:

``````-2.7777777777777777 * 729 = -2025
``````

Let us check:

``````var decimal_value_2 = numbase.parse( "b3:_10.1_1:1_10" );
// -2025
``````
• `numbase.str( <float>, <base> )` converts a JavaScript float value to a string in the given base. Example:
``````var balanced_ternary_string = numbase.str( -25, "b3" );
// "b3:_101_1"
``````

Parse & write real numbers in any base, including balanced bases.

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