$2\mathrm{.}5$ Exercises

$0.$ Review questions

$($a$)$ What is a normalized floating point number and what is the purpose of normalization?

$($b$)$ A general floating point system is characterized by four values $(,t,L,U).$ Explain in a

few brief sentences the meaning and importance of each of these parameters.

$($c$)$ Write down the floating point representation of a given real number $x$ in a decimal sys$-$

tem with $t=4,$ using $($i$)$ chopping and $($ii$)$ rounding.

$($d$)$ Define rounding unit $($or machine precision$)$ and explain its importance.

$($e$)$ Define overflow and underflow. Why is the former considered more damaging than the

latter?

$($f$)$ What is a cancellation error? Give an example of an application where it arises in a

natural way.

$($g$)$ What is the rounding unit for base $=2$ and $t=52$ digits?

$($h$)$ Under what circumstances could nonnormalized floating point numbers be desirable?

$($i$)$ Explain the storage scheme for single precision and double precision numbers in the

IEEE standard.