I could answer questions like this in two different ways, both of which might be correct and true.
The first way is the materialistic way, where I could explain that there’s no particular limit to what you could compute with zeros and ones. If a machine is Turing-complete, then it can compute anything that’s possible to compute, it might just take some time. The things we believe to be uncomputable involve things like infinities and paradoxes, not things like feelings. Feelings are reactions to inputs. You’re scared when you notice something potentially harmful, in pain when you’re damaged in any way, and angry when something violates your perception of what’s fair. In artificial intelligence, preferred outcomes are encoded as “utility functions”. An advanced AI might attach some kind of “feelings” to their utility function: they attach good feelings to high values, and bad feelings to low values of their utility function. This way, all feelings can be expressed as computations. (Note that in living beings, many feelings also have a chemical basis, as hormones and such, which can affect the brain’s computational processes in strange ways. Would still be possible to represent this as computations, though, just very complicated ones.)
The other way is the spiritual way, of course. Even if feelings can be computed, there might still be something that transcends the brain. Something that’s conscious, that has a sense of identity, “I am me”, and which is more than the body it’s in. No scientist has yet been able to pinpoint what causes this. They tend to assume, without proof, that it must be an emergent property of the extremely complicated system that’s the physical brain. It’s not an unreasonable assumption, I’d be inclined to agree with it myself. But from what I’ve seen, I’m not so sure it can really be reduced to that, as there are a number of phenoma that appear to falsify it. So, even if feelings might just exist in the physical brain, it seems your core consciousness (including some of your memories) could be rooted in a connection to something else in the universe. If the universe itself is alive, then our consciousnesses might be linked to its life force. (Although we still need our brains in order to exist physically.)