# floating point (FP)

In the early years of computer processing, a distinction was made in the representation of results between operations with fixed point and floating point( FP).

In floating point representation, the decimal point is included in the result. In order to keep the result representation with decimal point clear with a high number of digits, one changes over to a semi-logarithmic value representation. Here, the decimal places are usually represented in powers of 10. In this arithmetic operation, the number 0.000 045 could also be written as '45*10^-6', or the number 35,500 as '35.5*10^3'.

The value before the multiplication sign is the mantissa, the 10 is the base, which is exponentiated and then multiplied by the mantissa, and the superscript, the exponent. Applied to computing, the representation can be limited to the mantissa and the exponent if the base is 10. Thus, the representation of the first number would be 45E-6 and the second 35.5E+3, where the "E" stands for the exponent.

Floating point numbers are defined in the IEEE standard IEEE P754. The standard recognizes two formats with different precision and different value range, which are based on a 32-bit or 64-bit number. While the 64-bit format allows calculations with 18 decimal places, the 32-bit format allows more efficient and faster calculations.