Question $3$: A Floating$-$Point System for Melting Points of Metals $(16$ points$)$

You are asked to design a $16-$bit floating point number system to store the melting points $($in degrees Celsius$)$ of various metals. The value can be positive or negative.

This system should follow the similar design of the IEEE$754$ standard, with implicit $1,$ bias, normalized, de$-$normalized and special cases. Assume that the highest melting point to be stored is $+3422\mathrm{.}0$ degrees Celsius, and the lowest melting point to be stored is $-38\mathrm{.}829$ degrees Celsius.

a$)$ What is the minimum number of bits needed for the exponent? What is the value of the corresponding bias? Show your steps and reasoning process clearly, otherwise no point will be given. $(6$ points$)$