The mantissa is linear. It's unrelated to how positional number systems work. A floating point value is split into two numbers - the exponent and the mantissa. Normally they are used to represent a final number like:
x = 2^e * (1 + m)
Where e is the exponent and m is the mantissa (varying linearly from 0 to 1).
But you could have a fully exponential number format:
x = 2^(m + o)
As pointed out though, it makes addition much more complicated, you can't exactly represent integers, and someone told me it makes quantisation noise worse too. Bad idea.
But you could have a fully exponential number format:
As pointed out though, it makes addition much more complicated, you can't exactly represent integers, and someone told me it makes quantisation noise worse too. Bad idea.