Write the Boolean expression for the function (W) that corresponds to an irrigat

Question

Write the Boolean expression for the function (W) that corresponds to an irrigation system. The system should turn the water on when the soil humidity is low. Irrigation should not occur when it's raining or during the day. It's more efficient to irrigate at night so the water doesn't evaporate. The system is automated based on the rules above. However, the user has two switches to override the automation. The force-on switch (SI), when turned on, activates the irrigation without regard to the rules above. Similarly, the force-off switch (S2), when turned on, stops the irrigation and overrides the automation rules. Write the Boolean expression of W using the five variables below.

Explanation / Answer

W = S1 AND (NOT)S2 AND (((NOT)H AND R)OR((NOT)H AND L))

This table ensures, that the irrigation happens, when its dark, and not raining. Whereas, the enforcing switches, S1, and S2 should be added. If S1, i.e., when force-on switch is set, irrigation should happen. And if S2, i.e, when force-off switch is set, irrigation should not happen.

So, W = S1 OR (!S2 AND Z)

W = S1 OR(!S2 AND ((!H AND !R)AND(!H AND !L))).

If you need any refinement, just get back to me.

H(1) L(2) R(3) !H AND !R(4) !H AND !L(5) (4)AND(5) (Z) 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 x x 0 1 0 1 x x 0 1 1 0 x x 0 1 1 1 x x 0

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