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Python program to convert floating to binary

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  • Difficulty Level : Medium
  • Last Updated : 15 Jun, 2022
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Python doesn’t provide any inbuilt method to easily convert floating point decimal numbers to binary number. So, Let’s do this manually. Approach : To convert a floating point decimal number into binary, first convert the integer part into binary form and then fractional part into binary form and finally combine both results to get the final answer. For Integer Part, keep dividing the number by 2 and noting down the remainder until and unless the dividend is less than 2. If so, stop and copy all the remainders together. For Decimal Part, keep multiplying the decimal part with 2 until and unless 0 left as fractional part. After multiplying the first time, note down integral part and again multiply decimal part of the new value by 2. Keep doing this until reached a perfect number.  

Above steps can be written as : 1(base 10) = 1(base 2) and .234(base 10) = .0011(base 2) Now, to get the binary of 1.234, merge both results as a complete number. (1)10 = (1)2 (.234)10 = (.0011)2 (1.234)10 = (1.0011…)2 (1.234)10 = (1.0011)2  [approx.]

Below is the implementation : 


# Python program to convert float
# decimal to binary number
# Function returns octal representation
def float_bin(number, places = 3):
    # split() separates whole number and decimal
    # part and stores it in two separate variables
    whole, dec = str(number).split(".")
    # Convert both whole number and decimal 
    # part from string type to integer type
    whole = int(whole)
    dec = int (dec)
    # Convert the whole number part to it's
    # respective binary form and remove the
    # "0b" from it.
    res = bin(whole).lstrip("0b") + "."
    # Iterate the number of times, we want
    # the number of decimal places to be
    for x in range(places):
        # Multiply the decimal value by 2
        # and separate the whole number part
        # and decimal part
        whole, dec = str((decimal_converter(dec)) * 2).split(".")
        # Convert the decimal part
        # to integer again
        dec = int(dec)
        # Keep adding the integer parts
        # receive to the result variable
        res += whole
    return res
# Function converts the value passed as
# parameter to it's decimal representation
def decimal_converter(num):
    while num > 1:
        num /= 10
    return num
# Driver Code
# Take the user input for
# the floating point number
n = input("Enter your floating point value : \n")
# Take user input for the number of
# decimal places user want result as
p = int(input("Enter the number of decimal places of the result : \n"))
print(float_bin(n, places = p))

Output :

Enter your floating point value : 
Enter the number of decimal places of the result :

Enter your floating point value : 
Enter the number of decimal places of the result : 


Time Complexity : O(logn)

Auxiliary Space: O(1) if we use stack or arrays then O(logn) space will required 

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