Floating Point Visually Explained

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 {{< m “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 {{< m “2^{23} = 8388608” >}} possibilities) that matches the remainder as closely as possible.
The “default” IEE754 definition (Mantissa, Exponent, Sign): $(-1)^S * 1.M * 2^{(E-127)}$
$\pi$ translated to its IEE754 representation, step-by-step: