The European Centre for Medium$-$Range Weather Forecasts $($ECMWF$)$ has installed a

number of sensors in weather monitoring stations in the UK to measure temperature, light

levels, and daily rainfall levels. The sensors can measure temperatures in the range $-30$oC to

$+50$oC with precision $0\mathrm{.}2$oC$,$ the light intensity in the range of $0-1000$ lux $($lumens per square

meter$)$ with precision $0\mathrm{.}1$ lux and the daily rainfall expressed on a scale $0-5$cm with precision

$1$mm$.$ The sensors communicate their measurements to a ground station through a radio link.

$($a$)$ Determine how many bits and $8-$bit bytes are required to represent

$($i$)$ the temperature measurement $[3\%]$

$($ii$)$ the light intensity measurement $[3\%]$

$($iii$)$ the daily rainfall $[3\%]$

Justify your answer.

$($b$)$ Consider that an $8-$bit successive approximation ADC $($analogue to digital$)$ converter is

used for the conversion of temperature measurements. What would be the binary

representation of the temperature value $0\mathrm{.}8$oC$?$ Show all the steps of the conversion.

The reference temperature value is $40$

oC$.[10\%]$

$($c$)$ Consider the converted by the $8-$bit ADC temperature value in Question B$3($b$).$ If this

value is encoded by a $(7,4)$ Hamming code to protect it from possible bit errors, what

would be the resulting codeword? Encode the codeword in groups of four bits. $[6\%]$

$($d$)$ Consider that the encoded by Hamming codes temperature measurement in Question

B$3($c$)$ is transmitted over an unreliable radio link that introduces bit errors with

probability $10-3$

$.$ Would you say that the added protection is sufficient to correct the bit

errors if errors should be corrected with a probability of $99\%?$