An electronic switch that uses digital logic is to be developed for switching the lights on and off in an art gallery. The switch has to be turned on at 7:00 p.m. and turned off at 6:00 a.m. Also, if there are people in the gallery and the light that enters the gallery from outside is inadequate,

Question

An electronic switch that uses digital logic is to be developed for switching the lights on and off in an art gallery. The switch has to be turned on at 7:00 p.m. and turned off at 6:00 a.m. Also, if there are people in the gallery and the light that enters the gallery from outside is inadequate, the lights have to be turned on regardless of the time of the day. Assume that a sensor detects the presence of people in the gallery and produces a logic state of high (1). Also, there is sensor that detects the level of light entering the gallery from outside and generates a logic state of high (1) when the light level is inadequate. Furthermore, a digital clock produces logic high state when the time is between 6:00 a.m. to 7:00 p.m. Design a logic circuit that uses NAND gates only to operate the switch.

Accepted Answer

The logic state of the people sensor is denoted by p, that of the light sensor is denoted by l, and that of the time sensor is denoted by t. The output of the logic circuit is denoted by s, which is high (1) when the switch has to be on. The logic of the operation is, the switch has to be on when there are people in the gallery “and” the light entering from outside is not adequate, “or” if the time is not between 6:00 a.m. to 7:00 p.m. This statement translates into the Boolean relation

[latex]s=p\cdot l +\overline{t}[/latex]

Now, in order to determine a realization with NAND gates only, we proceed as follows:

[latex]s=p\cdot l +\overline{t} =\overline{\overline{p\cdot l+\overline{t}} } =\overline{\overline{p\cdot l} \cdot t} [/latex] (by double negation and application of the De Morgan law)

It is seen that this relation can be realized using two NAND gates, as shown in Figure 8.9.

Question 8.6: An electronic switch that uses digital logic is to be develo...

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