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In what ways can an analog multiplexer i.c fail? I want to use this in our system ,so i need the complete details of it,so that even if the mux fails,the output should connect to one of the input signals. Is this possible?

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It's likely not possible. The most common failure modes for ICs in my experience are for a pin to fail open-circuit, or short-circuited to either power or ground. For an IC to fail with one I/O pin connected to another one is very unlikely.

To get the behavior you want, you'd have to design an ancillary circuit that detects a failure condition (it would have to detect all possible failure conditions) and activates a second multiplexer to select input from the fail-over input instead of from the first mux. And then you'd have to worry about failure modes of that mux...and so on.

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