I'm currently a junior in college, and I read this last year by suggestion of another student who said it was an excellent precursor to our college's Computer Organization course (haven't taken it yet, so I don't know). It was also one of the books given to one of the CS department's Outstanding Seniors last year.
The beginning is a little slow if you know some physics, but it picks up and gets really interesting.
It's not simplistic at all. It's easy to understand, but it goes fairly in depth as to the internals of computing.
It has a very incremental approach. It starts with Morse code, Braille, numbering systems, moves on to logic gates, Boolean logic until it reaches microprocessors, character encoding, operating systems and finally some notes on high-level languages.
It's renowned as a classic anywhere you go. Very entertaining, too. It has a casual writing style.
[1] http://www.microsoft.com/mspress/books/sampchap/4677.aspx