Arbitrary precision number base conversion library
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Arbitrary Precision Base Converter

BaseConversion is a PHP library for converting number bases, similar to PHP's built in function base_convert(). However, unlike the built in function, this library is not limited by 32 bit integers and is capable of converting numbers of arbitrary precision. This library also supports conversion of fractions and allows more customization in terms of number bases.

In order to optimize the conversion of large numbers, this library also employs two different conversion strategies. In some cases, it's possible to convert numbers simply by replacing the digits with digits from the other base (e.g. when converting from base 2 to base 16). This is considerably faster than the other strategy, which simply calculates the new number using arbitrary precision integer arithmetic.

The API documentation, which can be generated using Apigen, can be read online at:

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In order to use this library, the following requirements must be met:

  • PHP version 5.4
  • GMP extension must be enabled


This library can be installed by using Composer. In order to do this, you must download the latest Composer version and run the require command to add this library as a dependency to your project. The easiest way to complete these two tasks is to run the following two commands in your terminal:

php -r "readfile('');" | php
php composer.phar require "riimu/kit-baseconversion:1.*"

If you already have Composer installed on your system and you know how to use it, you can also install this library by adding it as a dependency to your composer.json file and running the composer install command. Here is an example of what your composer.json file could look like:

    "require": {
        "riimu/kit-baseconversion": "1.*"

After installing this library via Composer, you can load the library by including the vendor/autoload.php file that was generated by Composer during the installation.

Manual installation

You can also install this library manually without using Composer. In order to do this, you must download the latest release and extract the src folder from the archive to your project folder. To load the library, you can simply include the src/autoload.php file that was provided in the archive.


The most convenient way to use this library is via the baseConvert() static method provided by the BaseConverter class. In most cases, it works the same way as base_convert() does. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;
echo BaseConverter::baseConvert('A37334', 16, 2); // outputs: 101000110111001100110100

The method accepts negative numbers and fractions in the same way. An optional fourth parameter can be used to define the precision for the conversion. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('-1BCC7.A', 16, 10)  . PHP_EOL; // outputs: -113863.625
echo BaseConverter::baseConvert('-1BCC7.A', 16, 10, 1); // outputs: -113863.6

The static method is simply a convenient wrapper for creating an instance of BaseConvert and calling the setPrecision() and convert() methods. If you need to convert multiple numbers, it's more efficient to call the object in a non static manner. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

$converter = new BaseConverter(16, 10);

echo $converter->convert('A37334') . PHP_EOL; // outputs: 10711860
echo $converter->convert('-1BCC7.A')  . PHP_EOL; // outputs: -113863.625

echo $converter->convert('-1BCC7.A'); // outputs: -113863.6

If the provided number contains invalid digits that are not part of the defined number base, the method will return false instead.

Converting Fractions

While this library does support conversion of fractions, it's important to understand that fractions cannot always be converted accurately from number base to another the same way that integers can be converted. This is result of the fact that not all fractions can be represented in another number base.

For example, let's say we have the number 0.1 in base 3. This equals the same as 1/3 in base 10. However, if you were to represent 1/3 as a decimal number, you would get an infinitely repeating '0.3333...'. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('0.1', 3, 10)  . PHP_EOL; // outputs: 0.33
echo BaseConverter::baseConvert('0.1', 3, 10, 6)  . PHP_EOL; // outputs: 0.333333
echo BaseConverter::baseConvert('0.1', 3, 10, 12); // outputs: 0.333333333333

Due to this behavior, it is possible to set the precision used for inaccurate fraction conversions. As can be seen in the previous example, the precision value defines the maximum number of digits in the resulting number. The result may have less digits, however, if the number can be accurately converted using a small number of digits. The precision may also be completely ignored, if the converter knows, that it can accurately convert the fractions.

The precision value also has an alternative definition. If the precision is 0 or a negative number, then the maximum number of digits in the resulting number is based on the precision of the original number. If the precision is 0, the resulting number will have as many digits as it takes to represent the number in the same precision as the original number. A negative number will simply increase the number of digits in addition to that. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('0.A7', 16, 10, 0)  . PHP_EOL; // outputs: 0.652
echo BaseConverter::baseConvert('0.A7', 16, 10, -2); // outputs: 0.65234

In the previous example, the original number is 0.A7 in the base 16. A base 16 number with two digits in the fractional part can represent a number up to accuracy of 1/(16 * 16) == 1/256. To represent the the fractional part in the same accuracy in base 10, we need at least 3 digits, because two digit can only represent numbers up to accuracy of 1/100.

The default precision value used by the library is -1. It is also important to note that the last digit is not rounded (due to the fact that it would cause inconsistent results in some cases).

Case Sensitivity

In order to make user interaction with the library more convenient, the library treats all numbers in a case insensitive manner, unless the number base prohibits that. For example, the base 16 can be treated in a case insensitive manner, because it only defines the value for the digits 0-9A-F. However, base 62 cannot be treated in a case insensitive manner, because letters like A and a have a different value.

The returned numbers will always respect the character case defined by the number base. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('7BFA11', 16, 12)  . PHP_EOL; // outputs: 2879B29
echo BaseConverter::baseConvert('7bfa11', 16, 12); // outputs: 2879B29

Customizing Number Bases

One of the features of this library is that allows much better customization of number bases than base_convert(). In most cases, you will probably define the number base using a simple integer such as 10 or 16. However, there is no limit to the size of that integer. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('7F', 16, 1024)  . PHP_EOL; // outputs: #0127
echo BaseConverter::baseConvert('5Glm1z', 64, 512); // outputs: #456#421#310#371

For large number bases, however, the digits are simply represented by a string that consists of # and the value for the digit. Whenever the number base is defined using an integer, the digits follow the following rules:

  • Bases equal or smaller than 62 use digits from the string 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
  • A base 64 number uses digits from the base64 standard, i.e. ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/
  • Other bases equal or smaller than 256 use bytes as digits with byte value indicating the digit value.
  • Large bases use strings for digits that consist of # and the value for the digit (the length of the string depends on the greatest digit value).

In addition to defining the number base using an integer, it's also possible to define the number base using a string. Each character in the string represents a digit and the position of each character represents it's value. The base 16, for example, could be defined as 0123456789ABCDEF. Defining number bases this way also makes it easier to get resulting numbers in a specific case. For example:


require 'vendor/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('101100011101', '01', 16)  . PHP_EOL; // outputs: B1D
echo BaseConverter::baseConvert('101100011101', 2, '0123456789abcdef'); // outputs: b1d

There is also a third way to define the number bases using an array. This allows even greater customization in terms of number bases. Each value in the array represents a digit and the index indicates the value. For example:


require 'src/autoload.php';
use Riimu\Kit\BaseConversion\BaseConverter;

echo BaseConverter::baseConvert('22', 10, ['nil', 'one'])  . PHP_EOL; // outputs: oneniloneonenil
echo BaseConverter::baseConvert('187556', 10, ['-', '-!', '-"', '-#', '', '-%']); // outputs: -¤---¤-!-%-"


This library is copyright 2013 - 2015 to Riikka Kalliomäki.

See LICENSE for license and copying information.