3 Beam Alarm

Cecelia is tired of nosy siblings and snooping parents entering her room undetected and so she is using her knowledge of digital electronics to develop an alarm system. Currently she is securing the doorway and has saved up enough money to purchase an infrared beam detection device. The device can be mounted on her doorway and has 3 detection beams at different heights: Beam A is at the lowest height. Beam B is the next highest beam. Beam C is the top most detection beam. When a beam is broken, a logic true(1) is reported to her selection circuit which must use combinational logic to determine whether or not to activate the alarm, W(output a logic 1 to activate). Obviously, if no beams are broken the alarm(W) should not be activated, however, grown ups, or anyone entering the room who trip all 3 beams should activate the alarm as should younger siblings and pets who trip only the first beam. In addition, Cecelia, or her friends, would like to pass through the doorway without activating the alarm so interruption of the lowest two beams should not activate the alarm. Cecelia considers activation of only one individual beam other than the lowest beam to be a nuisance and so the alarm should not sound in these cases either. For any other combination not specified here, the alarm should activate but a second output(F), should be set to logic true(1) to indicate that a fault may be present with one of the sensors. After spending her money on the sensor, Cecelia only has a collection of NAND gates and NOR gates to build the circuit so she will implement the Warning output using only 74LS00 two-input NAND gates, and the Fault detector out of only 74LS02 two-input NOR gates. Help Cecelia design her alarm circuit.