The Tower Crane $[50$ marks$]$

The tower crane is equipped with a digital logic circuit that controls the trolley hook, allowing it to move payloads in eight directions: north, northeast, east, northwest, west, southeast, southwest, and south, across four levels of a four$-$story tower. The signal AB functions as a $2-$bit logic indicator to determine if the trolley hook is reaching the correct floor, as specified by the floor$-$level indicator signals L$1,$ L$2,$ L$3,$ and L$4.$ The signal CDE operates as a $3-$bit logic indicator to verify whether the actuator in the trolley hook is moving in the correct direction among the eight possible directions. The output of the digital logic circuit is signal Z$.$ When Z is LOW $($logic $\text{'}0\text{'}),$ it indicates that the location is not one of the designated construction areas where the trolley crane can place the payload. However, when Z goes HIGH $($logic $\text{'}1\text{'}),$ it signifies a specific desired construction destination where the trolley hook is intended to deposit the payload