Python Program to Convert Floating Point Decimal to Binary

Decimal vs Binary

The decimal numeral system in which numbers are expressed in scales of 10. Whereas the binary numeral system involves expressing numbers in scales of 2.

Procedure

Step 1: The whole number part(59) of 59.65625 is divided by 2 until the quotient is 1. The remainder(carry) that is accumulated(either 1 or 0) till the last sequence of operation that gives the quotient 1 is taken in the reverse order of creation, so as to obtain 111011. 

59/2 = 29 (1 is taken as carry) 

29/2 = 14 (1 is taken as carry) 

14/2 = 7 (0 is taken as carry) 

7/2 = 3 (1 is taken as carry) 

3/2 = 1 (1 is taken as carry) 

So when we reverse the carry, we get 11011. Finally, we place the final quotient at the very beginning of the 11011 to get 111011.

Step 2: The decimal part is multiplied by 2 as many times as the number of decimal places in the final result required. To elaborate, let's take the above mentioned example of 59.65625. Here 0.65625 = 65625 * 10^-5. 

0.656252 = 1.31250 (1 is taken as carry) 

0.312502 = 0.62500 (0 is taken as carry) 

0.625002 = 1.25000 (1 is taken as carry) 

0.250002 = 0.50000 (0 is taken as carry) 

0.50000*2 = 1.00000 (1 is taken as carry)
When we bring the calculations together, we obtain 111011.10101

Source Code

def dec2bin(num):

    """"

    Function to convert a floating point decimal number to binary number

    """

    global wholeList

    global decList

    whole, dec = str(num).split('.')

    whole = int(whole)

    dec = int(dec)

    counter = 1

    

    while (whole / 2 >= 1):

            i = int(whole % 2)

            wholeList.append(i)

            whole /= 2

            

    decproduct = dec      

    while (counter <= places):

        decproduct = decproduct * (10**-(len(str(decproduct))))

        decproduct *= 2

        decwhole, decdec = str(decproduct).split('.')

        decwhole = int(decwhole)

        decdec = int(decdec)

        decList.append(decwhole)

        decproduct = decdec

        counter += 1

        

wholeList = []

decList = []

try:

    num = float(input('Enter a floating point decimal number: '))

    

except(ValueError):

    print('Please enter a valid floating point decimal')

try:

    places = int(input('Enter the number of decimal places in the result: '))

    dec2bin(num)

    if(len(wholeList) > 1):

        wholeList.reverse()

    wholeList.insert(0, 1)

    

    aster = '*'

    print(aster * 60)

    

    print('The binary number of {0} is:' .format(num))

    print(*wholeList, end =' ')

    print('.', end = ' ')

    print(*decList)

    

    print(aster * 60)

        

except(ValueError):

    print('Please enter a valid integer number for places')

Output

GitHub Link

https://github.com/pbipin/floatingpointdecimaltobinary

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