Floating point number formats can be normalized or not, meaning that ‘normal’ floating point numbers have an implicit (hidden) leading bit 1 in the significand. For example, the binary IEEE 754 formats are normalized, but the decimal IEEE 754 formats are not, i.e., they have an explicit leading bit (or number).
The advantage I see is the larger range or precision possible. (Larger range if compared to a format with one less exponent bit; greater precision if compared to a format with one less significand bit.)
However, the downsides I see are:
Dealing with a more complex format during computations, e.g., normalization steps, the existence of subnormals.
The loss of significance information. With, e.g., decimal IEEE 754 formats, the number of significand digits can be expressed. This would be a very useful feature, e.g., when encoding measurements. I would think that such information could also be exploited during computations.
On the whole, I feel that the larger range or greater precision that can be got with one extra bit does not justify the loss of a qualitative aspect, significance information. So my question is:
What are (other) reasons for or against using a normalized floating point format?
Perhaps the reason is historical and now the choice would be different; also this information is of interest to me. Perhaps the arguments I gave are not valid; it would then be interesting to know why.