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I'm looking for an online book that I came across a few years ago. It was free and it had the same type of material as covered in Petzold's "Code" - that is, how computers work on a fundamental level, starting from logic gates.

+1  A: 

I found it! How Computers Work by Roger Young.

Shawn J. Goff
A: 

I know you asked about a good free book, but here is a great free video lecture series on the exact topic you are asking about. It even includes such topics as how microprocessors and memory are designed. Otherwise, it goes into the same areas as Petzold's Code and it is free: Computer Architecture

Michael Goldshteyn