All the neurons in the brain that make up perceptions and emotions operate in a binary fashion. Eventually we'll be able to sequence the human genome and replicate how nature did intelligence in a carbon-based system. But the experience goes beyond analytic description.
Evolution is many orders of magnitude ahead of mankind today in creating a complex system.
I don't think it's irreconcilable to say we will understand the human mind some day and explain it in software-like terms, and also to say it is a creation that shouldn't be compared to software. Religion has come around to the view that even things that can be explained scientifically can have an underlying purpose that goes beyond the science. Even though I am not religious, the amazement and wonder I have about the human mind is closer to religious awe than dispassionate analysis. It seduces smart people into thinking they can't lose. And it's an unreliable guide to the future.