# How to convert an integer in any base to a string?

### 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

1
183
5/23/2017 12:34:43 PM

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 < 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 < 0:
digits.append('-')

digits.reverse()

return ''.join(digits)
``````
89
3/13/2018 12:18:51 AM

Surprisingly, people were giving only solutions that convert to small bases (smaller then 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