The information content of a mind cannot exceed the amount of information necessary to specify a representation of that same mind. Therefore, while the AI can understand in principle that it is made up of transistors etc., its self-representation necessary has some blank areas.

This is strictly true if you're talking about the working memory that is part of a complete model of your "mind". But a mind can access an unbounded amount of externally stored data, where a complete self-representation can be stored.

A Turing Machine of size N can run on an unbounded-size tape. A von Neumann PC with limited main memory can access an unbounded-size disk.

Although we can only load a part of the data into working memory at a time, we can use virtual memory to run any algorithm written in terms of the data as a whole. If we had an AI program, we could run it on today's PCs and while we could run out of disk space, we couldn't run out of RAM.