As I understand, digital cameras have a unity gain ISO: an ISO setting at which no gain is applied. Below this ISO negative gain is applied, in effect ignoring some of the photons, and above positive gain is applied.

Say for example we have a camera sensor with a 8 bit depth, unity gain ISO at 800, and positive gain is applied analog before the ADC. If an exposure is taken at ISO 1600, will the analog gain result in more quantization levels than if the photo were taken at ISO 800 and then bumped up a stop in post? That is, if the exposure is digitally increased a stop in post, the resulting histogram would be expected to have gaps. A DN of 1 would become 2, 2 to 4, 3 to 6 but there would be no output of 3, 5, etc. but if the gain is applied analog before the ADC, is there the extra data available to fill in those gaps?

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Yes, your conclusion is basically the case. That's one reason to do analog amplification and/or to have greater bit depth in your RAW conversion than your final state.

However, your definition of "unity gain" is not in line with, e.g., this one. See How does "Unity Gain ISO" differ from Native ISO?, and note that in most cameras, the "negative amplification" case is a special setting (often something like "Lo") if available at all. The base ISO is usually 100 or 200.

In practice, this is really not a big concern, because the ADC in most digital cameras is 12 or 14 bits, and there's pretty good evidence that this doesn't matter in the real world. See this blog post for examples, including extremely contrived worst-case situations.

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