The hex() Method in Python

Python's hex() method offers a way to obtain the hexadecimal representation of a floating-point number. Consider this:

obj.hex()

Here, "obj" denotes a floating-point number, or simply, a float.

The hex() method then returns a string encapsulating the float's hexadecimal form.

It's worth noting that this method is exclusive to float objects, meaning it's not applicable to integers.

Let's delve into an illustrative example.

Set the decimal value of 7.5 to the variable "num".

num = 7.5

Now, invoke the hex() method on "num".

num.hex()

This action produces the following hexadecimal output for the number 7.5

'0x1.e000000000000p+2'

This notation comprises two distinct parts: the hexadecimal and the exponential.

Here's a breakdown:

• 0x
  The "0x" prefix is a standard indicator of a base-16 number.
  

  '0x1.e000000000000p+2'

• 1.e000000000000
  The segment "1.e000000000000" is the heart of the hexadecimal representation. The portion before the dot "." signifies the whole number, while what follows the dot represents the hexadecimal fraction. In this context, 1.e in hexadecimal corresponds to 1.875 in our familiar decimal system.
  

  '0x1.e000000000000p+2'

  But how? The digit "1" occupies the units' place. In decimal terms, "1" in hexadecimal consistently equates to 1. The character "e" is positioned right after the hexadecimal point. In the hexadecimal system, "e" is synonymous with the number 14 (given that a=10, b=11, c=12, d=13, e=14, f=15). Since it's immediately after the point, it signifies the fraction 14/16 or 0.875 in decimal. Combining these components, we arrive at: $$ 1 + 0.875 = 1.875 $$

• p+2
  The notation "p+2" introduces the exponential component of our hexadecimal number. The character "p" is a precursor to a base-2 exponent. The accompanying "+2" suggests that our hexadecimal figure should undergo multiplication by 2^2, which is 4.
  

  '0x1.e000000000000p+2'

Thus, when 1.e in hexadecimal (or 1.875 in decimal) is multiplied by 4, the result is a familiar 7.5 in decimal.

$$ 1.e \cdot 2^2 = 1.875 \cdot 4 = 7.5$$

In essence, the num.hex() method provides a precise mechanism to articulate a floating-point number in the hexadecimal base.