Given a floating point system $(,$ t$,$ L$,$ U$)=(10,4,3,3),$ where is the base, t is the num$-$ ber of significant digits, L and U are the lower and upper bound of the exponent respectively.$($a$)(2$ points$).$ What are the floating point representation of the real numbers x $=4\mathrm{.}312809$ and y $=0\mathrm{.}4312809$ if the rounding strategy is used? What are corresponding relative errors$|$fl$($x$)$x$|$ and $|$fl$($y$)$y$|?($note that the first digit d$0=0)|$x$||$y$|($b$)(1$ point$).$ What is the rounding unit of this floating point system?$($c$)(1$ point$).$ Which of the following four numbers will cause the problem of underflow or overflow if it is represented by this floating point system?$($A$)0\mathrm{.}0051$; $($B$)0\mathrm{.}00000001$; $($C$)12000$; $($D$)12000.($d$)(1$ point$).$ Suppose that the above floating point system is used to calculate the root of the quadratic equation ax$2+$bx$+$c $=0,$ with a $=200,$ b $=1000$ and c $=100.$ What numerical difficulty will arise and how to overcome the difficulty?