Well, first I would ask whether this question makes sense in the first place. Does consciousness have a scope? Does consciousness even exist? Or is that more of a name attributed to some pattern we recognize in our own way of thinking (but may not be universal)?

Also, would a person missing an arm, but having a robot arm they can control have their consciousness' "scope" extended to it? Given that people have phantom pains, does a physical body even needed to consider it your part?

Similarly, if we can compute consciousness on a chip, then the chip obviously contains that consciousness. You can experimentally determine to what extent this is true: for example, you can experimentally check if increasing the clock frequency of said chip alters the consciousness that it is computing. Or if changing the thermal paste that attaches it to its cooler does so. I don't know what the results of these experiments would be, but they would be quite clearly determined.

Of course, there would certainly be some scale, and at some point it becomes semantics. The same is true with human consciousness: some aspects of the body are more tightly coupled to consciousness than others; if you cut my hand, my consciousness will change more than if you cut a small piece of my bowel, but less than if you cut out a large piece of my brain. At what point do you draw the line and say "consciousness exists in the brain but not the hands"? It's all arbitrary to some extent. Even worse, say I use a journal where I write down some of my most cherished thoughts, and say that I am quite forgetful and I often go through this journal to remind myself of various thoughts before taking a decision. Would it not then be fair to say that the journal itself contains a part of my consciousness? After all, if someone were to tamper with it in subtle enough ways, they would certainly be able to influence my thought process, more so than even cutting off one of my hands, wouldn't they?