If you figure out that A + B = C, do you need to understand how you got A and B to truly have solved the problem? Can't you take this further and say, without understanding every possible underlying system in our universe, we understand nothing?
Then "nothing", you know the word, will mean nothing? I think what we can do is make observations and assertions. We then have degrees of certitude on how much is true about our observation and assertions.
If you were trapped inside a computer, then by reaching the "Binary Theory" you have basically unveiled the building stone of the Computer Universe. Everything is in bits in computers.
That's what we are trying to do with quantum mechanics and finding a unified theory for physics. The theory of everything.
Point is, if you discover the Binary Theory inside the Computer Universe, you don't unveil the whole truth. Bits are the "real" building blocks. But then everything is powered by electricity, processors, RAMs and human developers. A real sophisticated world which is itself quantum.
So a "Binary Theory" might explain "everything" inside the Computer Universe, but still is not "reality". Finding reality will require breaking outside of the binary world.