Numeric Calculus - Floating Point

Floating point representation

Standard way computers handle real numbers.

The mathematical theorem

A floating-point number is a sum of powers of 2. Any real number x can be approximated by

x = (−1)^s × (1 + f) × 2^{e − B}

Where:

• s: determines if the number is positive or negative.
• f (fraction/mantissa): binary representation to the precision, usually a fraction.
• e: the exponent, an unsigned integer that determines the magnitude.
• B: bias, a constant subtracted from the exponent so we can represent both very large and very small numbers.