Computational Maths - Normalised mantissa

Question

What does overflow and underflow of an normalised mantissa mean?

Answer 1

IMO they mean nothing. For two reasons:

First: There are no such things as normalised mantissas. A mantissa is a bit pattern and not normalised, in IEEE double/single format every bit pattern of 52 resp. 23 bits can be the mantissa of a normalised number (and also of a denormal or NaN!)

Second: Overflow or underflow are results of operations (addition, muliplication, rounding etc). Overflow/underflow occur if the result of such operation cannot be presented as a normalised number (e.g. for singles $10^{30}\times 10^{28}$ resp. $10^{-30}\times 10^{-28}$).