A home security system has a master switch that is used to enable an alarm, lights, video cameras, and a call to local police in the event one or more of six sets of sensors detects an intrusion. In addition there are separate switches to enable and disable the alarm, lights, and the call to local police. The inputs, outputs, and operation of the enabling logic are speciied as follows:

Find a minimum-gate-input cost realization of the enabling logic using AND and OR gates and inverters.

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Inputs Si, i = 0, 1, 2, 3, 4, 5: signals from six sensor sets (0 = intrusion de- tected, 1 = no intrusion detected) M: master switch (0 = security system enabled, 1 = security system disabled) A: alarm switch (0 = alarm disabled, 1 = alarm enabled) L: light switch (0 = lights disabled, 1 = lights enabled) P: police switch (0 = police call disabled, 1 = police call enabled) Outputs A: alarm (0 = alarm on, 1 = alarm off) L: lights (0 = lights on, 1 = lights off) V: video cameras (0 = video cameras off, 1 C: call to police (0 = call off, 1 = call on) = video cameras on) Operation If one or more of the sets of sensors detect an intrusion and the secu- rity system is enabled, then outputs activate based on the outputs of the remaining switches. Otherwise, all outputs are disabled.