$11-40.$ Design the ADC interface to a digital thermostat using an LM$34$ temperature sensor and the ADC$0804.$ Your system must measure accurately $(+-2$F$)$ from $50$ to $101$F$.$The LM$34$ puts out $0\mathrm{.}01$V per degree F $(0$F $=0$ V$).$

$($a$)$ What should the digital value for $50$F be for the best resolution?

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$($b$)$ What voltage must be applied to Vin?

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$($c$)$ What is the full$-$scale range of voltage that will come in$?$

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$($d$)$ What voltage must be applied to Vref$/2?$

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$($e$)$ What binary value will represent $72$F$?$

$($f$)$ What is the resolution in F$?$ In volts?