You have been tasked with designing a microcontroller$-$based temperature control mechanism using a radiator and an air conditioner. The temperature is sensed at intervals of $10$ s $.$ If the temperature is above $T_{t{h}_h\text{i}\text{g}\text{h}\text{,}}$ then the air conditioner is turned on until the next measurement cycle starts. If the temperature is below $T_{th}$ lew, the radiator is turned on$,$ again until the next measurement cycle. If the temperature falls between $\frac{?}{\text{b}\text{a}\text{r}}(T{)}_{A_{{?}_{?}}\text{l}\text{e}\text{w}}$ and $T_{c_{-}\text{h}\text{i}\text{g}\text{h}},$ the system idles.

a$)$ What sensing mechanism will you use for the above system, if used for i$)$ and industrial application with temperature values above $500$ degC and ii$)$ A home automation application with temperatures between $-20$ degC and $40$ degC $.$ What is the sensing principle for each sensor$?(4$ marks$)$

b$)$ Elaborate on the desired characteristics for the sensors$.(4$ marks$)$

c$)$ How will you interface the $2$ different sensors to a microcontroller? $(4$ marks$)$

d$)$ What can be the sources of error in the sensing mechanism? $(4$ marks$)$

e$)$ If the tolerable quantization noise is $100V,$ determine an appropriate

Va$.$ar and resolution for the ADC. $(4$ marks$)$