To safely observe the positions of two cylinders, you need two signals: one circuit, X, which is open only when both cylinders are in a safe position (two normally closed switches in parallel), and one circuit, Y, which is closed only when both cylinders are in a safe position (two normally open switches in series, Figure 1).

This redundancy enables the detection of errors, such as a short circuit within a cable. The Boolean-logic equations of these two circuits are X=+, and Y=A·B. The problem is that most small limit switches are SPDT (single-pole, double-throw) switches, with which you cannot configure the circuit of Figure 1. Using Boolean arithmetic, you can derive X=+=+, which corresponds to the schematic in Figure 2. You can easily make a circuit equivalent to that of Figure 2 using two ordinary SPDT limit switches (Figure 3).

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