Recall that computers can only store discrete values in memory.

  1. What does this imply for the storage of real (floating-point) numbers in computers?
  2. 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.

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