The argument you're describing seems to rely on the assumption of functionalism in philosophy of mind. This is the idea that what is important about the mind and mental states (like experiences or qualia) is not their physical substrate but their functional organization.
Your argument does seem to follow logically from the premises, but only if we assume that consciousness arises purely from the complex functioning of physical systems. It might go something like this:
Consciousness arises from the physical reality of brain activity (Premise 1).
Brain activity can be described as a complex, binary process of neurons firing or not firing (Premise 2).
We can hypothetically create a physical system (like a wooden board with pegs and balls) that mirrors the binary processing of the brain (Premise 3).
Therefore, if we recreate the functional organization of the brain in this different physical system, it should also have consciousness (Conclusion).
However, there are some challenges and counterarguments:
Consciousness might not be solely a product of binary processes. The brain isn't just neurons firing or not firing; it's also the unique structure and connectivity of these neurons, the different types of neurons, the chemicals they release and respond to, and much more. The argument simplifies the reality of the brain's operation.
Even if consciousness arises from the physical activity of the brain, it might not be reducible to or replicable in a binary system. This is because it might depend on specific physical properties of the brain that can't be replicated in other materials or systems.
There's the "hard problem" of consciousness, which is the question of why and how physical processes in the brain give rise to subjective experiences or qualia. Even if we could replicate the brain's functional organization in another system, we don't know if that would be enough to produce consciousness.
If we assume the opposite (P1 is false), it doesn't necessarily imply that consciousness is metaphysical or exists outside the physical plane. It could just mean that our understanding of consciousness and the physical brain is incomplete.