This problem considers the consequences of rounding using double precision. Assume the “round to nearest” rule is used, and if there is a tie then the smaller value is picked (this rule for ties is...

This problem considers the consequences of rounding using double precision. Assume the “round to nearest” rule is used, and if there is a tie then the smaller value is picked (this rule for ties is used to make the problem easier).

(a) For what real numbers
 will the computer claim the inequalities 1
 <>

(b) For what real numbers
 will the computer claim
 = 4?

(c) Suppose it is stated that there is a floating-point number


_f

that is the exact solution of

²
− 2 = 0. Why is this not possible? Also, suppose


_f

and


_f

are the floats to the left and right ofrespectively. What doesequal?