I'm new to Python, and as I was coding for Project Euler to develop my skills in this language, I needed a function for converting between two bases. I know that int() can convert anything to base 10, but before I looked for a Python module concerning this math, I thought it would be a good idea to try and code one myself. Please, let me know if there is anything inefficient or in bad style so that I can improve.
It can handle A-Z notation (input both lower- and uppercase), any bases between 2 and 36, and catches problems related in invalid bases.
Matt Laporte <firstname.lastname@example.org> 2008
Base conversion tools. Allows for A-Z notation for digits greater than 9.
from types import StringType
def inBase(num, base, fromBase = 10, result = ''):
Converts any number in fromBase to its representation in base.
Defaults to converting to base_num from base_10.
if result == '':
#First call checks and corrections.
if num == 0: return '0'
base = __check(base)
if fromBase != 10:
fromBase = __check(fromBase)
""" In order to maintain the simplicity of the actual
conversion, this converts the number to base_10. """
num = toBase10(num, fromBase)
fromBase = 10
if num < 0:
#Further simplification for the conversion component.
result = '-' + result
num = -1 * num
if num == 0: return result #Return the final result when num has been handled.
#Conversion. This builds up result and eats away at num.
thisDigit = num%base
if thisDigit > 9: thisDigit = chr(thisDigit + 55) #Accounting for A-Z digits.
else: thisDigit = str(thisDigit)
return inBase(num/base, base, fromBase, thisDigit + result)
Verifies that a given base is 2-9 or A-Z.
Converts any base from A-Z to 10-35 for numerical calculations.
Should be used in the form: base == __check(base).
if type(base) == StringType and ((ord(base) > 96) and (ord(base) < 123)):
#Correct a-z to A-Z
base = chr(ord(base)-32)
if type(base) == StringType and ((ord(base) > 64) and (ord(base) < 91)):
#Correct A-Z to 10-35
return (ord(base) - 55)
elif type(base) != type(1) or type(base) == StringType:
#Not an integer, or any string other than A-Z.
raise TypeError, 'invalid base type for inBase()'
if base <= 1 or base > 36:
raise ValueError, 'invalid base for inBase(): %s' % base
def toBase10(num, base):
Converts any number represented in base to its base_10 representation.
sum = 0
parseNum = str(num)
indices = range(len(parseNum)) #Exponents depend on digit place, indices necessary.
for i in indices:
#Add the decimal representations of the digits.
sum += int(parseNum[i])*base**int(indices[::-1][i])
p.s. I haven't found the Python standard library function for any of this yet. As well, having a little experience in C, C++, Java, etc, I can say that Python is amazing. This -- and I know to be careful -- mutability and interchangeability (that is heresy in C) makes everything so easy in Python.
Edit: I used timeit. Although toBase10 was an attempt to imitate int() for the purpose of experiment, it is 10-15 times slower, so using int() in place of toBase10: 1 million executions of inBase with fromBase = 10 took around 10 seconds, with fromBase != 10 took around 20. I think this is pretty bad...
As far as conversions are concerned there are a number of functions:
int(x [,base]) converts x to an integer
long(x [,base]) converts x to a long integer
float(x) converts x to a floating-point number
complex(real [,imag]) creates a complex number
chr(x) converts an integer to a character
unichr(x) converts an integer to a Unicode character
ord(c) converts a character to its integer value
hex(x) converts an integer to a hexadecimal string
oct(x) converts an integer to an octal string
Make sure you take note that int() and long() can take numbers of a different base, provided that you specify which base you are converting from, ie:
I would like to share this function that converts a number in base 10 to any base between 2 and 36. Originally it was limited to bases 2-16.
def convDecToBase(num, base, dd=False):
if not 2 <= base <= 36:
raise ValueError, 'The base number must be between 2 and 36.'
if not dd:
dd = dict(zip(range(36), list(string.digits+string.ascii_lowercase)))
if num == 0: return ''
num, rem = divmod(num, base)
return convDecToBase(num, base, dd)+dd[rem]
denary to any base (2 to 36) conversion
def den2anybase(number, radix):
well, most any base with a radix in the range of 2 to 36
given a denary integer number (base 10)
return the base radix representation as a string
# max base 36 can be represented by letters 0-9 and a-z
abc = "0123456789abcdefghijklmnopqrstuvwxyz"
if not 2 <= radix <= 36:
# Python3 syntax
raise ValueError("base radix must be from 2 to 36")
result = 
# negative number and zero
if number < 0:
number = -number
elif number == 0:
number, rdigit = divmod(number, radix)
# reverse list of characters
# join list characters to a string
# test the function
print(den2anybase(255, 16)) # ff
print(den2anybase(-255, 16)) # ff-
print(den2anybase(0, 16)) # 0
print(den2anybase(35, 36)) # z
print(den2anybase(6580, 36)) # 52s
print(den2anybase(255, 2)) # 11111111
# for base x to base y conversions
# use int(num_string, x) to get denary (base 10)
# then apply to den2anybase(denary, y)
# (remember base x and base y have a range of 2 to 36)
print(den2anybase(int('11111111', 2), 16)) # ff
print(den2anybase(int('52s', 36), 16)) # 19b4
print(int('19b4', 16)) # 6580