[GolDDranks]

Another visualization that blew my mind; I learnt this from a presentation that was about doing floats with FPGAs:

Think 32-bit floats as a 256-bit buffer interpreted as a fixed precision number, with the decimal point straight in the middle, but with the limitation that you can set only a continuous 24-bit window on that buffer to non-zeros.

Then, the 8 bits of the exponent determine where in the bit buffer that window points to, and the 23 (+1) bits are the contents of the window.