Consider a ternary, normalized floating$-$point number system that is base $3$ with rounding.

Analogous to a bit, a ternary digit is called a "trit." Assume that a hypothetical ternary

computer uses the following floating$-$point representation:

$s_m{s}_e{e}_1{e}_2{t}_1{t}_2{t}_3{t}_4$

where:

$s_m$ is the sign of the mantissa $(0$ for positive, $1$ for negative$),$

$s_e$ is the sign of the exponent $(0$ for positive, $1$ for negative$),$

$t_1,t_2,t_3,$ and $t_4$ are the trits $($ternary digits$)$ of the mantissa,

$e_1,e_2$ are the trits of the exponent $($an integer$),$

Each trit can be $0,1,$ or $2.$

Show all your work for all parts.

$($a$)$ What is the computer representation of $-{5\mathrm{.}729}_{10}$ in this system?

$($b$)$ What decimal value does $01112021$ represent in this system?

$($c$)$ What is the maximum positive $($non$-$zero$)$ number that can be represented in this

system? Provide its value in decimal.

$($d$))$ Let $q$ be a real number in the interval $[{81}_{10},{243}_{10}).$ If we need to represent $q$ in

this ternary floating$-$point system with some approximation $q^{*},$ what is the upper

bound on the absolute error of this representation? Provide your answer in decimal.