I'm trying to make floating point number systems a bit more intuitive for myself. There are a few things I am confused about, and I think the best way to clear up my confusions would be for someone could guide me through one question: How many numbers are there in a floating point number system (Given the base, precision, max exponent, and min exponent)?
This is what I am thinking:
I figure that the maximum possible number (realmax) divided by the smallest possible number (realmin) would give all of the possible positive numbers. Part of me also believes I could divide realmax by the smallest increment, machine epsilon (eps), to figure out how many numbers there are. Just looking at the differences in magnitude between eps (10^-16 for IEEE double precision) and realmin (10^-308), however, tells me this isn't true at all. I can't think of an intuition for why!
So the problem I am facing is determining the correct formula for realmax and realmin. The answer I get using my textbook's formulas differ radically from the one I got with wikipedia's formula.