Recall that computers can only store discrete values in memory.

- What does this imply for the storage of real (floating-point) numbers in computers?
- Now consider the IEEE-storage convention for real numbers in computers for
`real32`

,`real64`

, and`real128`

bit storage formats as illustrated below.Compute how many real numbers each of the above formats can represent.

- How many of these numbers are in the range $[0, 1)$ for each storage convention?
- What are the minimum and maximum possible representable real values in these conventions?
- Is there a way to represent numbers that are smaller than the minimum representable real numbers in these conventions?