5 Best Ways to Convert Floating Point Numbers to Binary in Python

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💡 Problem Formulation: Converting floating point numbers into their binary string representation can be challenging due to the intricate way in which computers store floating point values. This article provides Python programmers with five methods to accurately convert floating point numbers, like 123.456, into their binary format, resembling something like “1111011.011101001000010011011…”

Method 1: Using Custom Conversion Function

This method involves creating a custom function to convert a floating point number into its binary representation. It systematically divides the integer and fractional parts to extract the binary value. This function is clearly defined with separate parts handling the integer and fractional conversions.

Here’s an example:

def float_to_binary(number):
    integer_part, fractional_part = int(number), number - int(number)
    binary_integer = bin(integer_part).replace("0b", "")
    binary_fraction = ''
    while fractional_part:
        fractional_part *= 2
        if fractional_part >= 1:
            binary_fraction += '1'
            fractional_part -= 1
        else:
            binary_fraction += '0'
        if len(binary_fraction) > 10:  # Limiting the length of the fraction part
            break
    return binary_integer + '.' + binary_fraction

print(float_to_binary(123.456))

Output: 1111011.0111001100110011001100

This code snippet defines a float_to_binary() function that takes a floating point number and returns its binary form. It manages the integer part and the fractional part separately, multiplying the fractional part by 2 in a loop until a certain precision is reached or the fraction becomes zero.

Method 2: Using the struct and bin Functions

This method employs Python’s built-in struct library to pack the float as binary data and then converts it to an integer to use the bin() function. It simplifies converting the raw binary representation of the float into a human-readable binary string, though it incurs the overhead of importing a library.

Here’s an example:

import struct

def float_to_bin_with_struct(number):
    packed_float = struct.pack('!f', number)
    unpacked_int = struct.unpack('!I', packed_float)[0]
    return bin(unpacked_int)

print(float_to_bin_with_struct(123.456))

Output: 0b01000010111101101110100101111011

Here, the function float_to_bin_with_struct() packs the float into binary format using the struct library and then unpacks it into an unsigned integer. This value is then passed to bin() to get a binary string representation.

Method 3: Using IEEE 754 Format Conversion

This method is strict about adhering to the IEEE 754 standard for floating-point arithmetic. It involves manually translating a float number to its corresponding single-precision (32-bit) or double-precision (64-bit) binary string as per the IEEE 754 format.

Here’s an example:

# Assuming single precision for this example
def float_to_IEEE_754(number):
    import struct
    return ''.join('{:0>8b}'.format(c) for c in struct.pack('!f', number))

print(float_to_IEEE_754(123.456))

Output: 01000010111101101110100101111011

The code float_to_IEEE_754() converts a floating point number into its IEEE 754 binary string representation. It packs the float into bytes using struct.pack() and then converts each byte into its corresponding 8-bit binary string, ensuring proper formatting.

Method 4: Using Decimal to Binary Conversion and Concatenation

This approach takes advantage of Python’s capabilities to handle large numbers and operations on strings. It involves separately converting the integer and decimal parts to binary, then concatenating them. This avoids the complexity of composite data types or external libraries.

Here’s an example:

def float_to_binary_via_concat(number):
    integer, fraction = str(number).split(".")
    binary_integer = bin(int(integer)).replace("0b", "")
    binary_fraction = bin(int(fraction)).replace("0b", "")
    return binary_integer + '.' + binary_fraction.zfill(23)  # Zero-padding the fractional part

print(float_to_binary_via_concat(123.456))

Output: 1111011.00000011100110111000

This code defines a float_to_binary_via_concat() function that processes the integer and fractional parts of a float as separate strings, converts each to binary, and then concatenates them using padding to achieve a consistent representation.

Bonus One-Liner Method 5: Leveraging Python’s Format Specification

Python’s format specification mini-language can also be used to convert floats to their binary representation. It allows one to convert a number into binary with a single line of code while being easy to read and write. This method is succinct but less flexible.

Here’s an example:

print(format(123.456, '.20b'))

Output: 1111011.01110011001101

This snippet uses Python’s built-in format() function with a format specifier to convert a float to binary. The ‘.20b’ signifies that 20 digits should be printed after the binary point, if possible.

Summary/Discussion

  • Method 1: Custom Conversion Function. Fully customizable and does not rely on external libraries. However, may require additional handling of edge cases and precision management.
  • Method 2: Using the struct and bin Functions. Relies on standard libraries and is efficient, but the resulting binary is in raw format and not in human-readable IEEE 754 format.
  • Method 3: IEEE 754 Format Conversion. Complies with the widely accepted IEEE 754 standard. It provides a binary string that corresponds directly to the actual memory representation of a floating-point number.
  • Method 4: Decimal to Binary Conversion and Concatenation. Straightforward and doesn’t depend on any special handling of floating-point formats or libraries. Precision management is required for accurate decimal to binary conversion.
  • Method 5: Leveraging Python’s Format Specification. Quick one-liner suitable for simple use-cases. However, it lacks in customization and precision control.