the background for question - specifications of binary32 float
My question is about assumption, that first (leading) bit is always 1, so we do not need to store it. That's true, but it has another role in number.. we know, where it starts. So after extracting that first non-zero bit, we don't know where number starts, unless there's another non-zero bit right afterwards.
In that wiki article, they use number (1.100011)binary. So fraction is 100011 and we can build up that number back without problem. However, what about (1.000011)binary? we extract 1 and we're left with 000011, and as we can't store leading zeroes inside zero-initialized bitfield, we get 11. But what happens, when we want to build it back? we get 1.11 and that's wrong.
So how we can freely extract that leading bit in arbitrary number?