How much hardware understanding does one need to fully comprehend "Operating System" and "Computer Architecture" courses one takes as a computer science student?
At that level, the more you know the better, but the bare necessities are boolean logic design for computer architecture. Understand how do you design registers, adders, multiplexers, flip flops, etc. from basic logic units (and, or, clocks). You can probably understand operating systems starting from basic understanding of ASM, memory mapped IO, and interrupts.
EDIT: I'm not certain what you mean by "hardware", do you consider logic design to be hardware? Or were you talking about transistors? I suppose it wouldn't hurt to understand the basics of semiconductors, but architecture is abstracted above the real hardware level. I would also say that operating systems are abstracted above the architecture.
At the very basic level, you should know about Von Neumann architecture and how it maps onto real-life computers. Above that, the more the better. And not just the OS - in garbage collected & VM languages, how the heap, stack and instructions work and are executed, so you know what will perform bad and how to improve it to get the best out of the architecture.
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