A thermocouple $($temperature sensor$)$ has an output of between $0$ and $50mV$ over a measuring range of $200$ to $800C.$

a$.$ Calculate by how much the output of an $8-$bit ADC with a $0$ to $5V$ input range would change over the full input range of the thermocouple $($give the binary output of the ADC$).$

b$.$ What would the temperature resolution be$?$

b$.$ What would the temperature resolution be$?$

c$.$ Would this system be practical, why?

d$.$ Other than increasing the number of bits of the ADC, what could be done to improve the temperature resolution of the system?