$1.$ Vehicle detection Joops, called inductive$-$loop traffic detectors, can detect vehicles passing or arriving at a certain point, for instance approaching a traffic light or in motorway traffic. An insulated, electrically conducting loop is installed in the pavement $($figure below$-$left$).$ Detector uses a LC oscillator consist of a wire loop buried in the ground underneath the road surface $($L$),$ a capacitor bank $($C$)$ to detect vehicles $($figure below$-$right$).$ Presence of a car above the loop buried in the ground changes the inductance of the loop embedded in the road which then alters the operating frequency of the oscillator. If we limit the operation frequency of the LC oscillator between $20$ kHz to $120$ kHz ; using block diagrams, explain in detail how do you design this system using

a$)$ A microcontroller with clock frequency of $1$ MHz $,$ and $4,8,32$ pre$-$scaler options, and two $14-$bit counters.

b$)$ A microcontroller with clock frequency of $10$ MHz $,$ and $16,32,256$ pre$-$scaler options, and one $32-$bit counter.