I can understand a computer because I know about it on a functional level and could construct one. While I do not know how the semi conducters work (well, I do to a certian level know the theory on a chemical level, I don't have a great level of understanding) that dosn't matter, in fact for a function understanding I would not even know how to make a logic gate from a transistor. This is because the logic gate is a fundemental compenent of the computer, and the transistor is not.
Were I to discover another way to build a logic gate without a transistor, then I could easily rebuild the same computer with the same logic gates, without transistors, so logic gates are fundemental, transistors are not. This is why the photon powered computer is still a computer in the common meaning of the term, despite the fact that it lacts the electrons that computers depends on. So I can understand a computer without understanding an electron.
To calculate something, however, requires me to be able to predict what outcome a computer will produce. If I build a computer that only multiplied two numbers (And doing this with analog is a walk in the park compaired to digital, but possible in both) and then put in the numbers 2264567 and 948576 I could understand what the computer was doing to produce it's outcome, but I couldn't predict what outcome it would produce (Not without a pen and paper anyway, but then I'm using additional hardware apart from just my brain).