1. A museum has three rooms, each with a motion sensor (m0, m1, m2) that outputs 1 when motion is detected. At night, the only person in the museum is one security guard who walks from room to room. Create a circuit that sounds an alarm (by setting an output A to 1) if motion is ever detected in more than one room at a time (i.e., there must be an intruder).
(a) Show your K-map,
(b) Find all prime implicants,
(c) Find all essential or secondary essential prime implicants,
(d) Design the minimum sum of product circuit (use cover table if necessary),
(e) Further simplify the two-level circuit in
(d) using Boolean algebra,
(f) Draw the circuit diagram.
2. Repeat Question 1 above by changing 3 rooms to 10 rooms. Now, K-map will not work for you. How can you solve this problem? Since K-map cannot be used, you do not have to follow the steps above. Instead, try to solve this problem using the INVERSE of the alarm function (e.g., using a negative thinking). You just need to write a Boolean equation to generate output A, and discuss possible implementation issues. For example, usually, an AND gate has about 3 to 4 inputs, but your switching expression for output A might have at least a term with 10 inputs. Note that you do not need to give circuit diagram since the circuit size is too large.