Title: Numeric base converter that accepts arbitrary digits
Submitter: Drew Perttula (other recipes)
Last Updated: 2002/01/31
Version no: 1.0
Category: Algorithms

Description:

This is a traditional base converter with the twist that it
accepts any strings as the digits for the input and output bases.

Besides all the normal base-converts, you can now create compact
versions of huge numbers by converting them to a base that uses
all the letters and numbers for its digits, for example.

Source: Text Source

BASE2 = "01"
BASE10 = "0123456789"
BASE16 = "0123456789ABCDEF"
BASE62 = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789abcdefghijklmnopqrstuvwxyz"

def baseconvert(number,fromdigits,todigits):
    """ converts a "number" between two bases of arbitrary digits

    The input number is assumed to be a string of digits from the
    fromdigits string (which is in order of smallest to largest
    digit). The return value is a string of elements from todigits
    (ordered in the same way). The input and output bases are
    determined from the lengths of the digit strings. Negative 
    signs are passed through.

    decimal to binary
    >>> baseconvert(555,BASE10,BASE2)
    '1000101011'

    binary to decimal
    >>> baseconvert('1000101011',BASE2,BASE10)
    '555'

    integer interpreted as binary and converted to decimal (!)
    >>> baseconvert(1000101011,BASE2,BASE10)
    '555'

    base10 to base4
    >>> baseconvert(99,BASE10,"0123")
    '1203'

    base4 to base5 (with alphabetic digits)
    >>> baseconvert(1203,"0123","abcde")
    'dee'

    base5, alpha digits back to base 10
    >>> baseconvert('dee',"abcde",BASE10)
    '99'

    decimal to a base that uses A-Z0-9a-z for its digits
    >>> baseconvert(257938572394L,BASE10,BASE62)
    'E78Lxik'

    ..convert back
    >>> baseconvert('E78Lxik',BASE62,BASE10)
    '257938572394'

    binary to a base with words for digits (the function cannot convert this back)
    >>> baseconvert('1101',BASE2,('Zero','One'))
    'OneOneZeroOne'

    """

    if str(number)[0]=='-':
        number = str(number)[1:]
        neg=1
    else:
        neg=0

    # make an integer out of the number
    x=long(0)
    for digit in str(number):
       x = x*len(fromdigits) + fromdigits.index(digit)
    
    # create the result in base 'len(todigits)'
    res=""
    while x>0:
        digit = x % len(todigits)
        res = todigits[digit] + res
        x /= len(todigits)
    if neg:
        res = "-"+res

    return res

Discussion:

Motivation and application

I needed a system to include a reference number in an outgoing email, so that a reply email could be tracked to the original context. I'm betting that words in the subject line are the most likely to be returned in a reply email (as opposed to words in the body or headers), so I sought a way to compress/obfuscate my reference number into a word that would comfortably fit in the subject line. Now instead of 20020111152908/20020129120001, I can simply include "H6Xwq/IjmAf". It's shorter, less prone to tampering, and it looks more like a magic cookie than some MTA junk. In fact, I could boost the security even more by privately shuffling the order in which I use the letters as digits (instead of A==0, B==1, etc).

Other uses

I didn't find a base converter in python upon doing some quick searches, so perhaps this code would be useful for everyday conversions as well.