Problem description: In a car security system, we usually want to connect the siren in such a way that the siren will activate when it is triggered by one or more sensors. In addition, there will be a master switch to turn the system on or off. Let us assume that there is a car door switch D, a vibration detector switch V, and the master switch M. We will use the convention that when the door is opened D = 1, otherwise, D = 0. Similarly, when the car is being shaken, V = 1, otherwise, V = 0. Thus, we want the siren S to turn on, that is, set S = 1, when either D = 1 or V = 1, or when both D = 1and V = 1, but only for when the system is turned on, that is when M = 1. However, when we turn off the system, and either enter or drive the car, we do not want the siren to turn on. Hence, when M = 0, it does not matter what values D and V have, the siren should remain off.
Problem description:
In a car security system, we usually want to connect the siren in such a way that the siren will activate when it is triggered by one or more sensors. In addition, there will be a master switch to turn the system on or off. Let us assume that there is a car door switch D, a vibration detector switch V, and the master switch M. We will use the convention that when the door is opened D = 1, otherwise, D = 0. Similarly, when the car is being shaken, V = 1, otherwise, V = 0. Thus, we want the siren S to turn on, that is, set S = 1, when either D = 1 or V = 1, or when both D = 1and V = 1, but only for when the system is turned on, that is when M = 1. However, when we turn off the system, and either enter or drive the car, we do not want the siren to turn on. Hence, when M = 0, it does not matter what values D and V have, the siren should remain off.
Instruction:
Start by constructing a truth table, which is basically a precise way of stating the operations for the device. The table should have three input columns M, D, and V, and an output column S. The values under the S column can be obtained from interpreting the description of when we want the siren to turn on. When M = 0, we don’t want the siren to come on, regardless of what the values for D and V are. When M = 1, we want the siren to come on when either or both D and V is a 1. From the table, formulate the logic expression then construct the equivalent logic diagram.
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