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Decimal to Binary Conversion (Python)

by vegaseat on Jun 10th, 2005

Converting a decimal integer (denary, base 10) to a binary string (base 2) is amazingly simple. An exception is raised for negative numbers and zero is a special case. To test the result, the binary string is converted back to the decimal value, easily done with the int(bStr, 2) function.

Python Code Snippet (Toggle Plain Text)

# convert a decimal (denary, base 10) integer to a binary string (base 2)
# tested with Python24   vegaseat    6/1/2005
 
def Denary2Binary(n):
    '''convert denary integer n to binary string bStr'''
    bStr = ''
    if n < 0:  raise ValueError, "must be a positive integer"
    if n == 0: return '0'
    while n > 0:
        bStr = str(n % 2) + bStr
        n = n >> 1
    return bStr
 
def int2bin(n, count=24):
    """returns the binary of integer n, using count number of digits"""
    return "".join([str((n >> y) & 1) for y in range(count-1, -1, -1)])
 
# this test runs when used as a standalone program, but not as an imported module
# let's say you save this module as den2bin.py and use it in another program
# when you import den2bin the __name__ namespace would now be  den2bin  and the
# test would be ignored
if __name__ == '__main__':
    print Denary2Binary(255)  # 11111111
 
    # convert back to test it
    print int(Denary2Binary(255), 2)  # 255
 
    print
 
    # this version formats the binary
    print int2bin(255, 12)  # 000011111111
    # test it
    print int("000011111111", 2)  # 255
 
    print
 
    # check the exceptions
    print Denary2Binary(0)
    print Denary2Binary(-5)  # should give a ValueError

Comments on this Code Snippet

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Sep 17th, 2005

Re: Decimal to Binary Conversion (Python)

Added an explanation for testing with
if __name__ == '__main__':

vegaseat

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Oct 21st, 2009

Re: Decimal to Binary Conversion (Python)

Well...if you are a newbie (like me), here is another solution, although not the best (A better way is certainly the first one on this page).( indentation lost after pasting it here. indent appropriately for the code to work)

#!/usr/bin/env python
import dectobin #Module...defined later
import string #Module.....defined later
a=int(raw_input("Enter a decimal number: "))
if a<0:
print "Try entering a positive number/0 "
elif a==0:
print "Binary: 0"
else:
list=dectobin.conv(a)
list1=string.format(list)
print "Binary: " ,list1

#!/usr/bin/env python
#This function takes an integer as arguement and returns binary equivalent as a list
def conv(a):
bin=[] #Define an empty list which will hold binary values
while(a!=1): #You want to keep dividing your integer with 2 until the quotient becomes 1
b=a%2 #Ccollect remainder.....it will be either 0 or 1
bin.append(b) # Hold this value in the empty list defined earlier
a=a/2

bin.append(1) #The last 1 which will remain after successive division
return bin
#!/usr/bin/env python
def format(list):
j=" " # Define an empty string
for i in range(0,len(list)): # list will have the binary values separated by comma
s=repr(list[i]) #Change each integer to string
j=j+s #Add it to an empty string
j=j[::-1] #Reverse the string
return j

Last edited by armored saint; Feb 16th, 2010 at 10:06 am. Reason: Formatting lost while copying

armored saint

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Feb 17th, 2010

Re: Decimal to Binary Conversion (Python)

There are 1000 ways to do this, and you just added way #1001

vegaseat

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Feb 17th, 2010

Re: Decimal to Binary Conversion (Python)

Here's a simple version using the bin() builtin while giving the same formatting options as the original example. Everyone has their own version of this, yet I still have yet to find a place where a string of the binary version of a number is useful.

Python Syntax (Toggle Plain Text)
def binary(n, digits=8):
    rep = bin(n)[2:]
    return ('0' * (digits - len(rep))) + rep
def binary(n, digits=8):
    rep = bin(n)[2:]
    return ('0' * (digits - len(rep))) + rep

GothAlice

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Feb 17th, 2010

Re: Decimal to Binary Conversion (Python)

About the formatting in the previous example, you can also use the format operator

python Syntax (Toggle Plain Text)
def binary(n, digits=8):
    return "{0:0>{1}}".format(bin(n)[2:], digits)
def binary(n, digits=8):
    return "{0:0>{1}}".format(bin(n)[2:], digits)

See this snippet about the marvels of format().

Last edited by Gribouillis; Feb 17th, 2010 at 3:14 pm.

Gribouillis

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Feb 17th, 2010

Re: Decimal to Binary Conversion (Python)

Lambda always intrigues me:

Python Syntax (Toggle Plain Text)
# works with IronPython, Python2 and Python3
 
d = 255
# a recursive dec to bin function
d2b = lambda d: (not isinstance(d,int) or (d==0)) and '0' \
    or (d2b(d//2)+str(d%2))
 
print(d2b(d))  # 011111111
# works with IronPython, Python2 and Python3

d = 255
# a recursive dec to bin function
d2b = lambda d: (not isinstance(d,int) or (d==0)) and '0' \
    or (d2b(d//2)+str(d%2))

print(d2b(d))  # 011111111

Lardmeister

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Aug 14th, 2011

Utility of string of binary version of number.

@ vegaseat: Thank you. Are you also vegasclimb?

@GothAlice:

"where string of the binary version is useful"?
For generating 1D fractals: http://tatetech.blogspot.com/2011/08/generating-1d-quasi-sierpinski-fractal.html

Python Syntax (Toggle Plain Text)
#!/usr/bin/python   
 
""" make1DFractalBin.py                                                        
 
    arg1 = Natural(for order of fractal)        
 
    arg2 = Natural(in 512 -- 527, 576 -- 591, 640 -- 655, 704 --719,
 
         768 -- 783, 832 -- 847, 896 -- 911, 960 -- 975)  for mask)
 
    Generates a 1D fractal of order N,     
 
    where the fractal generated by 975 is   
 
    1. removing the middle third of each segment 
 
    2. stretching by 3                 
 
    equivalent to more complicated make1DFractal.py Natural 
 
"""
 
import sys
 
# convert a decimal integer to a binary string (base 2)
 
# tested with Python24 vegaseat 6/1/2005                
 
#                                                                              
 
def Denary2Binary(n):
 
  """convert denary integer n to binary string bStr"""
 
  bStr = ''
 
  if n < 0: raise ValueError, "must be a positive integer"
 
  if n == 0: return '0'
 
  while n > 0:
 
    bStr = str(n % 2) + bStr
 
    n = n >> 1
 
  return bStr 
 
  #                                  
 
def main():
 
  maskDec = 975 # generator for Sierpinski square  
 
  #Read commandline argument for order of fractal         
 
  if len(sys.argv) < 2:
 
    print "usage: $ python make1DFractalBin.py Natural(Order of fractal) [Natur\
 
al](default = 975, else see top of file for allowed generators)"
 
    sys.exit(2)
 
  else:
 
    order = int(sys.argv[1])
 
    print "Order of Fractal ordered: ", order, '\n'
 
    if len(sys.argv) ==3:
 
      maskDec = int(sys.argv[2])
 
  print "Generator = ", maskDec
 
  maskB = Denary2Binary(maskDec)
 
  print "Mask = \n",maskB
 
  iter = 0
 
  while iter < order:
 
    l = len(maskB)-1
 
""" multiply the mask by 2**(twice its binary length), and add its original value. This is equivalent to stretching it and removing middle third.
 
"""
 
    maskDec = maskDec*((3-1)**(2*l)) + maskDec
 
    maskB = Denary2Binary(maskDec)
 
    print maskB
 
    iter+=1
 
if __name__ == '__main__':
 
  main()
#!/usr/bin/python   

""" make1DFractalBin.py                                                        

    arg1 = Natural(for order of fractal)        

    arg2 = Natural(in 512 -- 527, 576 -- 591, 640 -- 655, 704 --719,

         768 -- 783, 832 -- 847, 896 -- 911, 960 -- 975)  for mask)

    Generates a 1D fractal of order N,     

    where the fractal generated by 975 is   

    1. removing the middle third of each segment 

    2. stretching by 3                 

    equivalent to more complicated make1DFractal.py Natural 

"""

import sys

# convert a decimal integer to a binary string (base 2)

# tested with Python24 vegaseat 6/1/2005                

#                                                                              

def Denary2Binary(n):

  """convert denary integer n to binary string bStr"""

  bStr = ''

  if n < 0: raise ValueError, "must be a positive integer"

  if n == 0: return '0'

  while n > 0:

    bStr = str(n % 2) + bStr

    n = n >> 1

  return bStr 

  #                                  

def main():

  maskDec = 975 # generator for Sierpinski square  

  #Read commandline argument for order of fractal         

  if len(sys.argv) < 2:

    print "usage: $ python make1DFractalBin.py Natural(Order of fractal) [Natur\

al](default = 975, else see top of file for allowed generators)"

    sys.exit(2)

  else:

    order = int(sys.argv[1])

    print "Order of Fractal ordered: ", order, '\n'

    if len(sys.argv) ==3:

      maskDec = int(sys.argv[2])

  print "Generator = ", maskDec

  maskB = Denary2Binary(maskDec)

  print "Mask = \n",maskB

  iter = 0

  while iter < order:

    l = len(maskB)-1

""" multiply the mask by 2**(twice its binary length), and add its original value. This is equivalent to stretching it and removing middle third.

"""

    maskDec = maskDec*((3-1)**(2*l)) + maskDec

    maskB = Denary2Binary(maskDec)

    print maskB

    iter+=1

if __name__ == '__main__':

  main()

For order 2 and generator 975 we get:

rtate-mn:paths rtate$ python make1DFractalBin.py 2 975

Order of Fractal ordered: 2

Generator = 975

Mask =

1111001111

1111001111000000001111001111

1111001111000000001111001111000000000000000000000000001111001111000000001111001111

Now all I have to do is "square it"!

tatetech

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since Aug 2011

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Nov 15th, 2011

Re: Decimal to Binary Conversion (Python)

A rather straightforward one-liner to do the same thing:

python Syntax (Toggle Plain Text)
>>> bin(10)[2:].rjust(8, '0')
'00001010'
>>> bin(10)[2:].rjust(8, '0')
'00001010'

whitelynx

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since Nov 2011

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