Edit: yes, the chapter list is very similar to http://csapp.cs.cmu.edu/2e/samples.html with some OS topics thrown in.
For real bottom-up learning, Petzold's Code is one of the highly recommended books.
It maybe heresy to say, but Knuth doesn't explain concepts very well, reading more like a dense formal paper demanding a postgraduate mathematical background rather than elucidating concepts magnificently with both formal and informal terms. That's okay: subject matter experts need not be expert technical writers or lecturers. It could be the basis of another body of work by another author to write a compendium explaining and interpreting the Latin "Bible" to the masses. :)
You need a foundation for you to start making sense and to connect the dots for even the basic assumptions and theories that you may come up with.
Another way to put it is you need to know numbers(or atleast a basic sense of what they are) before you do math.
edit: does look good, I'll dive in.
— E. W. Dijkstra
Computer[s] from the Bottom Up