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BaseX is a arbitrary base conversion library that, in addition to converting to/from integers, also supports encoding and decoding arbitrary binary data into and out of any base.

Many known bases are included, such as Bitcoin Base58.

BaseX is useful for generating human-friendly cryptographic tokens and ID's, and could even be usde for encoding, transmitting, and decoding binary data over binary-unsafe mediums.


Add this line to your application's Gemfile:

gem 'base_x'

And then execute:

$ bundle

Or install it yourself as:

$ gem install base_x


Let's convert some numbers.

# Emulate hex, just for fun.
BaseX.integer_to_string(241,  numerals: "0123456789abcdef")
# => "f1"
BaseX.string_to_integer("f1", numerals: "0123456789abcdef")
# => 241

# Bitcoin Base58 numerals. No O, 0, I, or l
BaseX.integer_to_string(456724510, numerals: "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz")
# => "hMqHX"
BaseX.string_to_integer("hMqHX",   numerals: "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz")
# => 456724510

# That was rather clumsy, so let's use the provided Base58 object
# => "hMqHX"

If you use a base more than once, make it a constant.

Base24Greek ="αβγδεζηθικλμνξοπρστυφχψω")

# => "ιψια"
# => 456724510


Use the encode and decode methods to convert arbitary binary data to and from the desired base.

BaseX::Base30L.encode("Hello World!")
# => "3xtzc85paptyrbdjgd27"
# => "Hello World!"

BaseX.encode("SOS", numerals: "01")
# => "010100110100111101010011"
BaseX.decode("010100110100111101010011", numerals: "01")
# => "SOS"

The encoding scheme is simple: BaseX treats the whole binary blob as one large big-endian binary number and then converts that number into the desired base. If the original binary had leading 0 bytes, leading "0"'s are added to the converted number.

Base10 ="0123456789")

Base10.encode("Hi")         # => "18537"
Base10.encode("\x00Hi")     # => "00018537"
Base10.encode("\x00\x00Hi") # => "0000018537"

Token Generation

BaseX is great for generating tokens for identification or cryptographic purposes.

require 'securerandom'

bytes = SecureRandom.random_bytes(16) # 128 bits

# => "347wbrazxkvj59atq5zh2fdk55e"
# => "SLrA71VABcvExTht6KLr89"

Provided Bases

BaseX provides some bases you can use right away.

Constant(s) Example (64-bit token) Numerals and Explanation
BaseX::Binary "1111110010001110001…" 0-1
BaseX::Base16 BaseX::Base16L BaseX::Hex BaseX::Hexadecimal "fc8e3c917d58368b" 0-9a-f
Lowercase hexadecimal.
BaseX::Base16U "FC8E3C917D58368B" 0-9A-F
Uppercase hexadecimal.
BaseX::Base30L "369be5e68tfqth" 2-9a-hj-km-np-tv-z
(0 1 i l o u omitted.)
A BaseX special. All characters that could be confused in uppercase or lowercase are removed, so it is suitable for case-insensitive tokens. See BaseX::CrockfordBase32 for why "u" is removed.
BaseX::Base30U "369BE5E68TFQTH" 2-9A-HJ-KM-NP-TV-Z
(0 1 I L O U omitted.)
Uppercase version of above. I think lowercase is easier to read.
BaseX::Base31L "s59ez2tk5bep7" 0-9a-hj-km-np-z
(0 1 i l o omitted.)
A BaseX special. All characters that could be confused in uppercase or lowercase are removed, so it is suitable for case-insensitive tokens. The "u" is retained.
BaseX::Base31U "S59EZ2TK5BEP7" 0-9A-HJ-KM-NP-Z
(0 1 I L O omitted.)
Uppercase version of above. I think lowercase is easier to read.
BaseX::RFC4648Base32 "PZDR4SF6VQNUL" A-Z2-7
(0 1 8 9 omitted.)
The base 32 numerals of RFC 4648.
BaseX::CrockfordBase32 "FS3HWJ5YNGDMB" 0-9A-HJ-KM-NP-TV-Z
(I L O U omitted.)
The numerals of Douglas Crockford's Base32 proposal. Crockford fears that allowing "u" may result in "accidental obscenity". What's the actually probability of a problem? I calculate that, with "u" as a possible numeral, a random 3-numeral string has about a 1/8000 chance of phonetically dropping the f-bomb on a viewer; a 128-bit token encoded in base32 has 26 numerals and thus 24 3-numeral strings, consequently about 1 in every 340 such tokens would be vulgar.
BaseX::Base58 BaseX::BitcoinBase58 "jF78uMwAKKg" 1-9A-HJ-NP-Za-km-z
(0 I O l omitted.)
The numeral scheme used in Bitcoin addresses.
BaseX::FlickrBase58 "Jf78UmWajjF" 1-9a-km-zA-HJ-NP-Z
(0 I O l omitted.)
The numeral scheme in Flickr short URLs. Same as Bitcoin, but lowercase preceeds uppercase.
BaseX::GMPBase58 "gE67qKs9IId" 0-9A-Za-v
(w x y z omitted.)
The numeral scheme used for base conversions in the GMP arbitary-precision math library.
BaseX::NewBase60 "W5pTz7hmhxF" 0-9A-HJ-NP-Z_a-km-z
(I O l omitted, _ added.)
A scheme by Tantek Çelik, originally for use in a URL shortener. The "_" still allows the whole text to be selected when double-clicking.
BaseX::Base62 BaseX::Base62DUL "LgLY9aNSIf5" 0-9A-Za-z
All alphanumeric characters: digits then uppercase then lowercase.
BaseX::Base62DLU "lGly9AnsiF5" 0-9a-zA-Z
All alphanumeric characters: digits then lowercase then uppercase.
BaseX::Base62LDU "vGv8jAx2sFf" a-z0-9A-Z
All alphanumeric characters: lowercase then digits then uppercase.
BaseX::Base62LUD "vQvIjKxCsPf" a-zA-Z0-9
All alphanumeric characters: lowercase then uppercase then digits.
BaseX::Base62UDL "VgV8JaX2SfF" A-Z0-9a-z
All alphanumeric characters: uppercase then digits then lowercase.
BaseX::Base62ULD "VqViJkXcSpF" A-Za-z0-9
All alphanumeric characters: uppercase then lowercase then digits.
BaseX::URLBase64 "PyOPJF9WDaL" A-Za-z0-9-_
(- _ added.)
Alphanumerics plus - and _. Intended as a base 64 that can be used in URLs; part of RFC 4648. I find URL base 64 annoying because double-clicking won't select through the -.
BaseX::Z85 "]MO]Dt%j>*" 0-9a-zA-Z.-:+=^!/*?&<>()[]{}@%$#
(. - : + = ^ ! / * ? & < > ( ) [ ] { } @ % $ # added.)
The base 85 numerals used for ZeroMQ Z85, an encoding standard optimized for 4-byte words and for pasting into single-quoted strings.
BaseX::Base256 "\xFC\x8E<\x91}X6\x8B" "\x00"-"\xFF"
Byte 0 through byte 255; useful for convert binary strings into a number and back. Used internally by BaseX.

Note that although the number schemes from various standards are represented here, BaseX is a number converter only: it does not do padding or other standard-specific details. BaseX is not, for example, a Z85 compliant encoder/decoder. You could, however, easily build one with BaseX.

In Ruby, you can uses BaseX.bases and BaseX.print_bases to get information similar to the above table.

> BaseX.print_bases
Binary          2   111111001000111000111… 01
Base16          16  fc8e3c917d58368b       0123456789abcdef
Base16L         16  fc8e3c917d58368b       0123456789abcdef
Base16U         16  FC8E3C917D58368B       0123456789ABCDEF
Hex             16  fc8e3c917d58368b       0123456789abcdef
Hexadecimal     16  fc8e3c917d58368b       0123456789abcdef
Base30L         30  369be5e68tfqth         23456789abcdefghjkmnpqrstvwxyz


In addition to the named constants above, you can also quickly generate any alphanumeric base between 2 and 62. This could be handy becuase Ruby's to_i and to_s methods only support bases 2 to 36.

# => "1UB4UI"
# => 456724510

# The order of numerals is digits then uppercase then lowercase
# => "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklm"

Use Base30L

If you want your text to be transferred by any means other than copy-paste, I recommend BaseX::Base30L. Tokens have a bad habit of landing in places where they cannot be copied and pasted. Anecdotal evidence from my recent past:

  • There was an infographic that had cited URLs baked into the image. I wanted to check the sources but could not copy the URLs, so I had to retype them. Also, some of the URLs had "O"'s in them.
  • I recently transferred a shared secret from one computer to another "off the wire". I had my mother read the secret out loud from the other computer. Happily, the secret did not have mixed case: saying "capital L, lowercase u" would have doubled the tedium.

You can't predict what people are going to do with your encoded text, so it makes sense to be prepared.

Edge Cases

Even though "".to_i is 0 in Ruby, BaseX's string_to_integer will reject empty strings with a BaseX::EmptyString error. An empty string here is probably a bug in your code. (In contrast, the encode and decode functions do accept empty strings.)

If you try to convert a string that uses a character not in the base, a BaseX::InvalidNumeral error will be raised.


If you try to encode/decode in a numeral system larger than base 256 (why would you do this?!), leading 0 bytes may not be properly preserved. Integer conversion will still work as expected.


Public Domain; no rights reserved.

No restrictions are placed on the use of BaseX. That freedom also means, of course, that no warrenty of fitness is claimed; use BaseX at your own risk.

Public domain dedication is explained by the CC0 1.0 summary (and only the summary) at


  1. Fork it ( )
  2. Create your feature branch (git checkout -b my-new-feature)
  3. Run the tests with either guard or minitest
  4. Commit your changes (git commit -am 'Add some feature')
  5. Push to the branch (git push -u origin my-new-feature)
  6. Create a new Pull Request