Resistor-Diode-Relay Logic Source Selector

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Among the many possibilities, here is one of the most minimalistic.

I requires a non-inverting tri-state buffer, and as many pull-up resistors as there are channels, plus three additional ones.

The active state (low in this example) is determined by the polarity of the output enable inputs.
This example has 8 channels, but it could be extended to ~∞ by simply duplicating the base circuit as many times as required

Some caveats: the outputs cannot be too heavily loaded compared to the 4.7K pullups (although the 4K7's could be used to drive PNP transistors, driving the relays).
The circuit will always start in a deterministic way, which is all channels off (it could start on one defined channel with a power-on circuit using one capacitor, one resistor and one diode).
The mode of operation is similar to mechanically interlocked push-buttons selectors: when a new channel is selected, it releases the currently active one(s), but if two channels are selected simultaneously, they both become active. This could be a problem, an advantage or indifferent.

In principle, the scheme is not limited to the 40244 or 74HC244, but I recommend a quick test before making other choices: the circuit is somewhat "irregular", and could have problems depending on the peculiarities of each IC.

Note that for an even more minimalist circuit, R10 and R11 could be dispensed with, but it could pose reliability issues.
 

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