Question 1: Let X = 11.00000 00000 00000 00000 011?;

(a) Why is it impossible to represent X exactly in 32-bit IEEE ?oating-point? (b) and (c) What are the two binary numbers closest to X that we *can* represent?

For problems 11 and 12, represent binary numbers using 5 signi?cant bits. (One way to do this is to always represent numbers as 1.bbbb?×?2? where the b's are bits and n is an exponent.
So we can't represent 100001 because that would be 1.00001 ? ×?2?. It also means we can't carry out the addition 100000 + 1 without truncation (of a nonzero bit).

Question 2: To calculate (.00001 + .00001) + 1.0000 requires two additions. (a) Does the ?rst addition, .00001 + .00001, cause truncation (of nonzero bits) before or after the addition? If so, specify how and when (b) Does the second addition, [the value from part a] + 1.0000?

Question 3: Repeat the previous question on .00001 + (.00001 + 1.0000). (Part a is the right-hand addition; part b is the left-hand addition.)

Solve these questions in details and provide examples to support your rationale.