Suppose in the IEEE single format, the width of the exponent field is 4, not 8, and the width of the fraction field is 4, not 23.

For part f) only give an example if the statement is false. If the statement is true then prove without using an example.

(f) (3 points) Given any three floating point numbers x, y and z in this system, is it always true that (x y) z = x @ (y z)? Either prove it or give a counterexample. (g) (2 points) Find a real x in the range of subnormal numbers such that (round(x) - x] |x| > 1 - 6 1 . 2 where the round to nearest mode is used. (f) (3 points) Given any three floating point numbers x, y and z in this system, is it always true that (x y) z = x @ (y z)? Either prove it or give a counterexample. (g) (2 points) Find a real x in the range of subnormal numbers such that (round(x) - x] |x| > 1 - 6 1 . 2 where the round to nearest mode is used