1. A car wash with two bays has a pump supplying water pressure to the spray hea

Question

1. A car wash with two bays has a pump supplying water pressure to the spray heads. If both bays are in use or if one bay requires a second set of heads for a tall truck, a second pump is required. The Tall truck request is made via a selector switch for each bay. If both bays are in use with a tall truck in one or both bays, a third pump is required. a) Write Boolean equations for the above: 1) Situation 1 (Bay 1 in Use or Bay 2 i Use): 2) Situation 2 (Bay 1 in Use and Bay 2 in Use or Bay 1 in Use and Tall Truck in Bayl or Bay 2 in Use and Tall Truck in Bay 2): 3) Situation 3 (Both bays are in use with a tall truck in one or both bays) b) Convert the Boolean equations to Ladder Logic: 1) Situation 1 Bay 1 in use run pump 1 Bay 2 in use

Explanation / Answer

From the data given above, we have total three pumps, and these three pumps turn on by meeting certain conditions.

Those conditions are,

condition 1: pump 1 runs if either of the bay spray heads is in use.

condition 2: pump 2 runs if Both the bays are in use or if one bay requires the second set of the selector switch for the tall truck

condition 3: pump 3 runs if both bays are in use with a tall truck in one or both bays

Now,

Let's represent bay1 with B1, bay2 with B2, pump1 with P1, pump2 with P2 and pump3 with P3And it's given 2-way two selector switches (S1 and S2) for each bay that means if the switch in position 1 (High) then position 2 will be Low.

That means it toggles between position 1 and 2.

Now let us form the boolean equations basing on the conditions

1. P1 is HIGH if B1 is HIGH or B2 is HIGH

2. P2 is HIGH if ( B1 is HIGH and B2 is HIGH) or (B1 is HIGH and S1 is HIGH) or B2 is HIGH and S2 is HIGH)

3. P3 is HIGH if ( B1 is HIGH, B2 is HIGH and S1 is HIGH) or (B1 is HIGH, B2 is HIGH and S2 is HIGH) or (B1 is HIGH, B2 is HIGH, S1 is HIGH and S2 is HIGH)

so,

P1 = (B1+B2)

P2 = (B1.B2)+(B1.S1)+(B2.S2)

P3 = (B1.B2.S1)+(B1.B2.S2)+(B1.B2.S1.S2)

= (B1.B2.S1)+(B1.B2.S2)+(B1.B2.S1.S2)+(B1.B2.S1.S2) {Since A+A = A}

= B1.B2.S1(1+S2) + B1.B2.S2(1+S1)   

= B1.B2.S1 + B1.B2.S2 { Since 1+A = 1}

= B1.B2(S1+S2)

The boolean equations for the three situations are

P1 = B1 + B2

P2 = B1.B2+ B1.S1+ B2.S2

P3 = B1.B2(S1+S2)

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