Exercise $6\mathrm{.}2$ Suppose that the destination format is IEEE single and the rounding

mode is round to nearest. What are $64o+2^{20},64o+2^{-20},32o+2^{-20},16o+2^{-20},8o+2^{-20}?$

Give your answers in binary, not decimal. What are the results if the rounding mode

is changed to round up$?$

Exercise $6\mathrm{.}3$ Recalling how many decimal digits correspond to the $24-$bit precision of

an IEEE single format number, which of the following expressions do you think have

the value exactly $1$ if the destination format is IEEE single and the rounding mode is

round to nearest: $1o+$round$({10}^{-5}),1o+$round$({10}^{-10}),1o+$round$({10}^{-15})?$

Exercise $6\mathrm{.}4$ What is the largest floating point number $x$ for which $1o+x$ is exactly $1,$

assuming the destination format is IEEE single and the rounding mode is round to

nearest? What if the destination format is IEEE double?