Answer 1

Float and Double primitive types are both normalized numbers, which work this way, storing the left hand as mantissa and the right as characteristics, using 2 as radix = M*r^k

Or if you wish, you can write your own (much slower) number type (class) based on the same concept. Depending on what you want to earn may in situations it can be useful.

Answering your question; yes, totally possible, the processor even has special parts to carry out calculation on numbers represented by binary exponents (the mentioned two primitives in Java).