A Cal Poly Pomona Mechanical Engineering student mounts an accelerometer having a sensitivity of $\backslash (2\mathrm{.}8\backslash$mathrm$\{$mV$\}/\backslash$mathrm$\{$g$\}\backslash )$ to one of Cal Poly's Mini$-$Baja front end struts. He has built a data acquisition system $($DAS$)$ using an operational amplifier, a passive low$-$pass RC filter, and an $\backslash (\backslash$mathrm$\{$A$\}/\backslash$mathrm$\{$D$\}\backslash )$ converter having $4$ bits and a full$-$scale excitation of $10$ Volts. He is sampling the data at a rate of $5000$ Hz $.$ On the memory of his DAS, the binary value of $0111$ corresponds to the magnitude of the voltage measured by the accelerometer. Unfortunately, his filter attenuates the signal by $5$ dB $.$ If the Op$-$Amp gain is set at $1000,$ determine$/$address the following:

$($a$)$ Neatly and accurately sketch a block$/$flow diagram of the DAS showing all major elements as described above

$($b$)$ Compute the voltage at each stage in the DAS and clearly label the diagram of part $($a$)$ with these computed voltage values

$($c$)$ Roughly, how many g$\text{'}$s does the value of $0111$ at the data acquisition board correspond to$?$