How to convert an integer to a string in any base

Question

Python allows easy creation of an integer from a string of a given base via   int str  base      I want to perform the inverse  creation of a string from an integer   i e  I want some function int2base num  base   such that   int int2base x  b   b     x   The function name argument order is unimportant    For any number x and base b that int   will accept   This is an easy function to write  in fact it s easier than describing it in this question  However  I feel like I must be missing something     I know about the functions bin  oct  hex  but I cannot use them for a few reasons    Those functions are not available on older versions of Python  with which I need compatibility with  2 2   I want a general solution that can be called the same way for different bases I want to allow bases other than 2  8  16   Related   Python elegant inverse function of int string  base  Integer to base-x system using recursion in python Base 62 conversion in Python How to convert an integer to the shortest url-safe string in Python

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A recursive solution for those interested  Of course  this will not work with negative binary values  You would need to implement Two s Complement   def generateBase36Alphabet        return    join  str i  for i in range 10    chr i 65  for i in range 26     def generateAlphabet base       return generateBase36Alphabet    base   def intToStr n  base  alphabet       def toStr n  base  alphabet           return alphabet n  if n  lt  base else toStr n  base base alphabet    alphabet n base      return   -  if n  lt  0 else       toStr abs n   base  alphabet   print     - gt      format -31  intToStr -31  16  generateAlphabet 16       -31 - gt  -1F

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Another short one  and easier to understand imo    def int to str n  b  symbols  0123456789abcdefghijklmnopqrstuvwxyz        return  int to str n b  b  symbols  if n  gt   b else       symbols n b    And with proper exception handling   def int to str n  b  symbols  0123456789abcdefghijklmnopqrstuvwxyz        try          return  int to str n b  b  if n  gt   b else       symbols n b      except IndexError          raise ValueError               The symbols provided are not enough to represent this number in                this base

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def int2base a  base  numerals  quot 0123456789abcdefghijklmnopqrstuvwxyz quot        baseit   lambda a a  b base   not a  and numerals 0   or baseit a-a b b base  numerals a b  base-1  or  a b  and  base-1       return baseit     explanation In any base every number is equal to  a1 a2 base  2 a3 base  3    The  quot mission quot  is to find  all a  s  For everyN 1 2 3    the code is isolating the  aN base  N by  quot mouduling quot  by b for b base   N 1    which slice all a  s bigger than N  and slicing all the a  s that their serial is smaller than N by decreasing a everytime the func is called by the current aN base  N   Base  base-1   1 therefor base  p  base-1   1 and therefor q base p  base-1   q with only one exception when q base-1 which returns 0  To fix that in case it returns 0 the func is checking is it 0 from the beggining   advantages in this sample theres only one multiplications  instead of division  and some moudulueses which relatively takes small amounts of time

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I made a pip package for this   I recommend you use my bases py https   github com kamijoutouma bases py which was inspired by bases js  from bases import Bases bases   Bases    bases toBase16 200                      gt   c8  bases toBase 200  16                    gt   c8  bases toBase62 99999                    gt   q0T  bases toBase 200  62                    gt   q0T  bases toAlphabet 300   aAbBcC           gt   Abba   bases fromBase16  c8                      gt  200 bases fromBase  c8   16                   gt  200 bases fromBase62  q0T                     gt  99999 bases fromBase  q0T   62                  gt  99999 bases fromAlphabet  Abba    aAbBcC        gt  300   refer to https   github com kamijoutouma bases py known-basesalphabets for what bases are usable  EDIT  pip link https   pypi python org pypi bases py 0 2 2

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This is an old question but I thought i d share my take on it as I feel it is somewhat simpler that other answers  good for bases from 2 to 36    def intStr n base 10       if n  lt  0     return  -    intStr -n base            handle negatives     if n  lt  base  return chr  48 55  n gt 9    n            48   gt   0      65   gt   A         return intStr n  base base    intStr n base base    recurse for multiple digits

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I know this is an old post  but I m just leaving my solution here just in case  def decimal to given base integer to convert  base        remainder   integer to convert    base      digit   integer to convert   base      if integer to convert    0           return  0       elif remainder    0           return str digit       else           return decimal to given base remainder  base    str digit

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gt  gt  gt  numpy base repr 10  base 3   101   Note that numpy base repr   has a limit of 36 as its base  Otherwise it throws a ValueError

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Great answers  I guess the answer to my question was  no  I was not missing some obvious solution   Here is the function I will use that condenses the good ideas expressed in the answers    allow caller-supplied mapping of characters  allows base64 encode  checks for negative and zero maps complex numbers into tuples of strings    def int2base x b alphabet  0123456789abcdefghijklmnopqrstuvwxyz         convert an integer to its string representation in a given base      if b lt 2 or b len alphabet           if b  64    assume base64 rather than raise error             alphabet    ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789            else              raise AssertionError  int2base base out of range       if isinstance x complex     return a tuple         return   int2base x real b alphabet    int2base x imag b alphabet        if x lt  0          if x  0              return alphabet 0          else              return   -    int2base -x b alphabet        else x is non-negative real     rets        while x 0          x idx   divmod x b          rets   alphabet idx    rets     return rets

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0 b   format 100    bin  1100100   0 x   format 100    hex  64   0 o   format 100    oct  144

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gt  gt  gt  import string  gt  gt  gt  def int2base integer  base           if not integer  return  0          sign   1 if integer  gt  0 else -1         alphanum   string digits   string ascii lowercase         nums   alphanum  base          res              integer    sign         while integer                  integer  mod   divmod integer  base                  res    nums mod          return     if sign    1 else  -     res   -1     gt  gt  gt  int2base -15645  23   -16d5   gt  gt  gt  int2base 213  21   a3

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Well I personally use this function  written by me  import string  def to base value  base  digits string digits string ascii letters        converts decimal to base n      digits slice   digits 0 base       temporary var   value     data    temporary var       while True          temporary var   temporary var    base         data append temporary var          if temporary var  lt  base              break      result          for each data in data          result    digits slice each data   base      result   result   -1       return result   This is how you can use it   print to base 7  base 2    Output   111   print to base 23  base 3    Output   212   Please feel free to suggest improvements in my code

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Here is an example of how to convert a number of any base to another base   from collections import namedtuple  Test   namedtuple  Test     n    from base    to base    expected      def convert n  int  from base  int  to base  int  - gt  int      digits          while n           n  r    divmod n  to base          digits append r          return sum from base    i   v for i  v in enumerate digits     if   name         main         tests             Test 32  16  10  50           Test 32  20  10  62           Test 1010  2  10  10           Test 8  10  8  10           Test 150  100  1000  150           Test 1500  100  10  1050000              for test in tests          result   convert  test  -1           assert result    test expected  f  test     result        print  PASSED

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def base decimal  base        list    0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ      other base          while decimal    0           other base   list decimal   base    other base         decimal      decimal   base     if other base                other base    0      return other base  print base 31  16    output       1F

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Here is a recursive version that handles signed integers and custom digits   import string  def base convert x  base  digits None          Convert integer  x  from base 10 to base  base  using  digits  characters as digits      If  digits  is omitted  it will use decimal digits   lowercase letters   uppercase letters              digits   digits or  string digits   string ascii letters      assert 2  lt   base  lt   len digits    Unsupported base      format base      if x    0          return digits 0      sign    -  if x  lt  0 else        x   abs x      first digits   base convert x    base  base  digits  lstrip digits 0       return sign   first digits   digits x   base

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def baseN num b numerals  0123456789abcdefghijklmnopqrstuvwxyz        return   num    0  and numerals 0   or  baseN num    b  b  numerals  lstrip numerals 0     numerals num   b     ref  http   code activestate com recipes 65212   Please be aware that this may lead to   RuntimeError  maximum recursion depth exceeded in cmp   for very big integers

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You could use baseconv py from my project  https   github com semente python-baseconv  Sample usage    gt  gt  gt  from baseconv import BaseConverter  gt  gt  gt  base20   BaseConverter  0123456789abcdefghij    gt  gt  gt  base20 encode 1234   31e   gt  gt  gt  base20 decode  31e    1234   gt  gt  gt  base20 encode -1234   -31e   gt  gt  gt  base20 decode  -31e    -1234   gt  gt  gt  base11   BaseConverter  0123456789-   sign       gt  gt  gt  base11 encode   1234     -22   gt  gt  gt  base11 decode   -22     1234    There is some bultin converters as for example baseconv base2  baseconv base16 and baseconv base64

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Surprisingly  people were giving only solutions that convert to small bases  smaller than the length of the English alphabet   There was no attempt to give a solution which converts to any arbitrary base from 2 to infinity  So here is a super simple solution  def numberToBase n  b       if n    0          return  0      digits          while n          digits append int n   b           n     b     return digits   -1   so if you need to convert some super huge number to the base 577  numberToBase 67854    15 - 102  577   will give you a correct solution   4  473  131  96  431  285  524  486  28  23  16  82  292  538  149  25  41  483  100  517  131  28  0  435  197  264  455   Which you can later convert to any base you want

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def dec to radix input  to radix 2  power None       if not isinstance input  int           raise TypeError  Not an integer        elif power is None          power   1      if input    0          return 0     else          remainder   input   to radix  power         digit   str int remainder to radix   power-1            return int str dec to radix input-remainder  to radix  power 1     digit   def radix to dec input  from radix       if not isinstance input  int           raise TypeError  Not an integer        return sum int digit   from radix  power  for power  digit in enumerate str input    -1     def radix to radix input  from radix 10  to radix 2  power None       dec   radix to dec input  from radix      return dec to radix dec  to radix  power

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I made my function to do this  Run well on windows 10  python 3 7 3  def number to base number  base  precision   10       if number    0          return  0           positive   number  gt   0     number   abs number           ints         store the integer bases     floats         store the floating bases      float point   number   1     number   int number      while number          ints append int number base           number     base     ints reverse            while float point and precision          precision -  1         float point    base         floats append int float point           float point   float point - int float point       return ints  floats  positive   def base to str bases  string  quot 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ quot         quot  quot  quot bases is a two dimension list  where bases 0  contains a list of the integers      and bases 1  contains a list of the floating numbers  bases 2  is a boolean  that s     true when it s a positive number      quot  quot  quot      ints          floats           for i in bases 0           ints append string i        for i in bases 1           floats append string i        if len bases 1    gt  0          return    quot - quot    quot  quot   bases 2      quot  quot  join ints      quot   quot      quot  quot  join floats       else          return    quot - quot    quot  quot   bases 2      quot  quot  join ints               Example   gt  gt  gt  base to str number to base -6 252  2    -110 0100000010

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Recursive  I would simplify the most voted answer to   BS  0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ  def to base n  b        return  0  if not n else to base n  b  b  lstrip  0     BS n b    With the same advice for RuntimeError  maximum recursion depth exceeded in cmp on very large integers and negative numbers   You could usesys setrecursionlimit new limit    Iterative  To avoid recursion problems   BS  0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ  def to base s  b       res          while s          res  BS s b          s    b     return res   -1  or  0

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def base conversion num  base       digits          while num  gt  0          num  remainder   divmod num  base          digits append remainder      return digits   -1

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If you need compatibility with ancient versions of Python  you can either use gmpy  which does include a fast  completely general int-to-string conversion function  and can be built for such ancient versions     you may need to try older releases since the recent ones have not been tested for venerable Python and GMP releases  only somewhat recent ones   or  for less speed but more convenience  use Python code     e g   most simply  import string digs   string digits   string ascii letters   def int2base x  base       if x  lt  0          sign   -1     elif x    0          return digs 0      else          sign   1      x    sign     digits           while x          digits append digs int x   base            x   int x   base       if sign  lt  0          digits append  -        digits reverse        return    join digits

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num   input  number   power   0 num   int num  while num  gt  10      num   num   10     power    1  print str round num  2           str power

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Strings aren t the only choice for representing numbers  you can use a list of integers to represent the order of each digit  Those can easily be converted to a string   None of the answers reject base  lt  2  and most will run very slowly or crash with stack overflows for very large numbers  such as 56789    43210   To avoid such failures  reduce quickly like this   def n to base n  b       if b  lt  2  raise   invalid base     if abs n   lt  b  return  n      ret    y for d in n to base n  b b  for y in divmod d  b       return ret 1   if ret 0     0 else ret   remove leading zeros  def base to n v  b       h   len v     2     if h    0  return v 0      return base to n v  -h   b     b  h    base to n v -h    b   assert    join   0123456789  x  for x in n to base 56789  43210 10     str 56789  43210    Speedwise  n to base is comparable with str for large numbers  about 0 3s on my machine   but if you compare against hex you may be surprised  about 0 3ms on my machine  or 1000x faster   The reason is because the large integer is stored in memory in base 256  bytes   Each byte can simply be converted to a two-character hex string  This alignment only happens for bases that are powers of two  which is why there are special cases for 2 8  and 16  and base64  ascii  utf16  utf32    Consider the last digit of a decimal string  How does it relate to the sequence of bytes that forms its integer  Let s label the bytes s i  with s 0  being the least significant  little endian   Then the last digit is sum  s i   256  i    10 for i in range n     Well  it happens that 256  i ends with a 6 for i   0  6 6 36  so that last digit is  s 0  5   sum s  6  10  From this  you can see that the last digit depends on the sum of all the bytes  This nonlocal property is what makes converting to decimal harder

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def base changer number base       buff 97 abs base-10      dic    buff2    buff3 10     for i in range 97 buff 1           dic buff3  chr i          buff3  1        while number gt  base           mod int number base          number int number  base          if  mod  in dic keys                buff2  dic mod              continue         buff2  str mod      if  number  in dic keys            buff2  dic number      else          buff2  str number       return buff2   -1

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def baseConverter x  b       s          d   string printable upper       while x  gt  0          s    d x b          x   x   b     return s   -1

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http   code activestate com recipes 65212   def base10toN num n          Change a  to a base-n number      Up to base-36 is supported without special notation         num rep  10  a            11  b            12  c            13  d            14  e            15  f            16  g            17  h            18  i            19  j            20  k            21  l            22  m            23  n            24  o            25  p            26  q            27  r            28  s            29  t            30  u            31  v            32  w            33  x            34  y            35  z       new num string        current num     while current  0          remainder current n         if 36 gt remainder gt 9              remainder string num rep remainder          elif remainder gt  36              remainder string     str remainder              else              remainder string str remainder          new num string remainder string new num string         current current n     return new num string   Here s another one from the same link  def baseconvert n  base          convert positive decimal integer n to equivalent in another base  2-36          digits    0123456789abcdefghijklmnopqrstuvwxyz       try          n   int n          base   int base      except          return         if n  lt  0 or base  lt  2 or base  gt  36          return         s          while 1          r   n   base         s   digits r    s         n   n   base         if n    0              break      return s

[python] How to convert an integer to a string in any base?

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