I really wish he didn't make [0,1] one of the windows, because in floating point arithmetic the range [0,1] contains approximately as many floating point numbers (a billion or so in Float32) as the range [1,∞). There are "windows" [2^k,2^(k+1)] for positive as well as negative k. Just creates unnecessary scope for further confusion.
In 32 bit float, about 50% of the possible values (no denormals) fall between -0.5 and 0.5 (~2 000 000 000), the space on each side between 0.5 and 1 adds only about 80 million new values.
