Consider an alarm system with five inputs: fire $($F$-011),$ water$-$tank$-$full $($W$-001),$ burglary $($B$100),$

smoke $($S$-111)$ and dust$($D$-010).$ For this alarm system an alarm signal $($A$)$ is on if any of these events

occur a three bit code is shown to denote the incident. In case of multiple events, a priority is followed

as: F $>$ B $>$ S $>$ D $>$ W$.$ For this alarm system, find out the simplified expression of the alarm signal $($A$)$

and the encoding bits for the associated $5\backslash$times $3$ priority encoder and draw the logic diagram.