Another problem with bin() on floats is that it will be a one-way street
because as far as I know, there is no function to convert a binary
string back to a float.

My last thought on this issue is that it will be helpful to add
tobase(f, n) and frombase(s,n) functions to math module (and I withdraw
my suggestion of using %g-like notation due to the conflict between E
for exponent and E for 0xE).  On the other hand, there is no need to
mess up with builtin bin/oct/hex because with math.tobase float-capable
extensions will be trivially implementable.