# Floating Point Visually Explained

*https://fabiensanglard.net/floating_point_visually_explained/index.html*

- Window/offset is a more intuitive way to think about IEE754 floating points compared to the usual exponent/mantissa.
I tend to agree, and this mental model makes the fact that you
*lose precision as the whole number portion of the decimal gets bigger*abundantly clear. - The window gets 1 byte, and represents any two consecutive powers of two.
- The offset gets 23 bits, and represents the range of values within the window (and can represent \(2^{23}\)) discrete values.
- To translate a decimal into floating point, find the right window that the whole number portion fits into. Find the offset (one of \(2^{23} = 8388608\) possibilities) that matches the remainder as closely as possible.
- The “default” IEE754 definition (
**M**antissa,**E**xponent,**S**ign):

$$
(-1)^S * 1.M * 2^{(E-127)}
$$

- \(\Pi\) translated to its IEE754 representation, step-by-step: