Why do we want to keep mantissa as small as possible and exponent as large as possible in the floating point representation of numbers?
What would happen if we make mantissa as big as possible?
Note:
https://www.youtube.com/watch?v=MQF1Bg-ykRA&list=PLYdroRCLMg5O-SZZL8kqFkcjWllPVpmXc&index=10
NUMERICALMETHODS FOR ENGINEERS, SIXTH EDITION by Chapra & Canale. Page-64 to 65
In floating point numbers, the mantissa is normalized so it is less than one in absolute value.
So this question is based on an incorrect assumption.
The representation is of the form $\text{mantissa} * \text{base}^{\text{exponent}}$ with the exponent usually biased so it fits more nicely into however many bits it uses.
The mantissa can be made smaller, usually by some power of the base, and this requires the exponent to be made correspondingly larger. These numbers are called un-normalized.
There is a whole lot more in the discussion of floating point arithmetic. Of course, Knuth has a bunch.
Another name to search for is Kahan.