Design a digital circuit for a hazard level display system in an industrial environment The system monitors 6 hazard sensors named S 0 through S 5 where SO indicates the least severe hazard S 5 indicates the most severe hazard Each sensor outputs logic 1 if it detects an active hazard The circuit takes 6 active high inputs S 5 S 4 S 3 S 2 S 1 and S 0 The outputs of the circuit are A 3 bit binary value A 2 A 1 A 0 representing the index 0 to 5 of the most severe active hazard sensor A hazard indicator bit H which is 1 if at least one sensor is active and 0 otherwise a Draw the truth table for this system b Based on the truth table clearly indicate which known combinational logic component if any the truth table represents c Derive the Boolean equation for the output bit A 1 only in minimized SOP or POS form