Question $1)(25$ points$)$ Consider $9$ bit word $($sign$,$ sign of exponent, $3$ bit for exponent, $4$ for mantissa$)$

hypothetical floating point representation.

a$)$ Find the $9$ bit representation of $(34\mathrm{.}50{)}_{10}$

b$)$ Compute the absolute relative true error $(lo{n}_a)$ of $(34\mathrm{.}50{)}_{10}$

c$)$ Find the machine epsilon $({}_{\text{m}\text{a}\text{c}\text{h}})$A machine stores floating point number in a $9-$bit word. The first bit is for the sign of the number, the second bit is for the sign of the exponent, the next $3$ bits are for the exponent, and the final $4$ bits are for the mantissa. The number that $(000011111)2$ represents in the above given $9-$bit format is