How Do Floating Point Numbers Work?

We often use floating-point numbers in programming, but have we ever thought about how they actually work?

Let’s take a look at the following binary number: 1111.1101

How is it converted to a decimal number?

🔹 Integer Part (1111)

Binary value: (1×8) + (1×4) + (1×2) + (1×1) = 15

🔹 Fractional Part (.1101)

Binary value: (1×1/2) + (1×1/4) + (0×1/8) + (1×1/16) = 0.8125

Final Conversion:

1111.1101 (Binary) = 15.8125 (Decimal)