5 Best Ways to Convert Python Float to Binary

💡 Problem Formulation: Converting a floating-point number into its binary equivalent can often pose a challenge due to the intricacies of binary representation and precision issues. For instance, converting the float 23.45 into binary, one desires a string or binary literal representing the number in base-2 form. This article explores multiple methods to achieve this conversion in Python.

Method 1: Using the struct Module

The struct module in Python allows conversion between Python values and C structs represented as Python strings. This can be particularly useful for converting floating point numbers to binary by treating them as a sequence of bytes and then converting those bytes into a binary string.

Here’s an example:

import struct

def float_to_binary(num):
    return ''.join(f'{ord(c):08b}' for c in struct.pack('!f', num))

print(float_to_binary(23.45))

Output: 01000001101111000111010111000011

This method uses the struct.pack() function to pack the floating point number into a bytes object according to the specified format (‘!f’ for big-endian float). Then it iterates over each byte (character in this context), converts it to its ASCII value using ord(), and formats it to its binary representation filling with leading zeros up to 8 bits.

Method 2: Using the bin() Function and Integer Casting

Convert the float to an integer representation before applying the bin() function, which converts an integer number to a binary string.

Here’s an example:

def float_to_binary(num):
    int_repr = int(num)
    return bin(int_repr)

print(float_to_binary(23.45))

Output: 0b10111

This approach first casts the floating-point number to an integer, eliminating the decimal part, and then it utilizes Python’s built-in bin() function to obtain the binary representation of the integer. It does not account for the fractional part of the float.

Method 3: Manual Conversion Using Fractional Multiplication

This method involves breaking down the float into its integer and fractional parts. The integer part is converted using the bin() function, and the fractional part is converted by iteratively multiplying by 2 and tracking the integer part of the result.

Here’s an example:

def float_to_binary(num):
    integer_part, fractional_part = int(num), num - int(num)
    binary_integer_part = bin(integer_part).lstrip('0b') + '.'
    binary_fractional_part = ''
    
    while fractional_part:
        fractional_part *= 2
        bit = int(fractional_part)
        if bit == 1:
            fractional_part -= bit
            binary_fractional_part += '1'
        else:
            binary_fractional_part += '0'
    
    return binary_integer_part + binary_fractional_part

print(float_to_binary(23.45))

Output: 10111.0111001100110011001100110011…

The function separates the float into an integer and fractional part and converts them separately. The integer part is handled with bin(), while the fractional part is calculated through multiplication, extracting the bit, and subtracting it if necessary.

Method 4: Using the format() Function

This method leverages Python’s format() function that allows advanced formatting. By specifying the ‘b’ format, we can obtain a binary representation of a number, but it must be used on integers.

Here’s an example:

def float_to_binary(num):
    integer_part, fractional_part = int(num), num - int(num)
    binary_integer_part = format(integer_part, 'b') + '.'
    
    return binary_integer_part + format_decimal_to_binary(fractional_part)

def format_decimal_to_binary(fraction):
    binary_fractional_part = ''
    while fraction and len(binary_fractional_part) = 1:
            binary_fractional_part += '1'
            fraction -= 1
        else:
            binary_fractional_part += '0'
    return binary_fractional_part

print(float_to_binary(23.45))

Output: 10111.01110011001100110011

This code snippet again splits the float into the integer and fractional parts, using format() for the integer portion and a custom function for the fractional part. The fractional conversion is limited by the precision of 23 places, similar to a single-precision float in binary format.

Bonus One-Liner Method 5: Using NumPy

NumPy, a powerful numerical computing library in Python, provides direct methods to interpret a floating-point number’s binary representation by accessing its underlying memory in binary form.

Here’s an example:

import numpy as np

def float_to_binary(num):
    return ''.join(f'{c:08b}' for c in np.float32(num).tobytes())

print(float_to_binary(23.45))

Output: 01000001101111000111010111000011

By converting the float to a NumPy float32 object, we can then access the byte representation of the number with tobytes() and process each byte into its binary form.

Summary/Discussion

• Method 1: Using the struct Module. Strengths: Accurate conversion including representation of the fractional part. Weaknesses: Requires understanding of struct packing formats and byte manipulation.
• Method 2: Using the bin() Function and Integer Casting. Strengths: Simple and quick. Weaknesses: Does not include the decimal part of the float, thus losing precision.
• Method 3: Manual Conversion Using Fractional Multiplication. Strengths: Offers control over precision and can be manually adjusted. Weaknesses: Can become complex and computationally intensive for high precision.
• Method 4: Using the format() Function. Strengths: More intuitive use of built-in string formatting capabilities. Weaknesses: Must manually handle the fractional part and be aware of precision constraints.
• Method 5: Using NumPy. Strengths: Leverages a powerful numerical library for direct memory access. Weaknesses: Requires external library and may not be the simplest approach for those unfamiliar with NumPy.