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 :
Python3
# Python program to convert float# decimal to binary number# Function returns octal representationdef 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 representationdef decimal_converter(num): while num > 1: num /= 10 return num# Driver Code# Take the user input for# the floating point numbern = input("Enter your floating point value : \n")# Take user input for the number of# decimal places user want result asp = int(input("Enter the number of decimal places of the result : \n"))print(float_bin(n, places = p)) |
Output :
Enter your floating point value : 1.234 Enter the number of decimal places of the result : 4 1.0011
Enter your floating point value : 11.234 Enter the number of decimal places of the result : 4 1011.0011
Time Complexity : O(logn)
Auxiliary Space: O(1) if we use stack or arrays then O(logn) space will required
