Prerequisites for operating systems and compiler design

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Bipolarity
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What would be the prerequisites for an operating systems course or for a compiler course? I am well-versed in C programming and digital circuit design but have very little knowledge of computer architecture. Would I be recommended to go through a text on comp arch before starting a text on OS/compiler design? Opinions?

Thanks!

BiP
 
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For compilers: my university requires data structures and (our introduction to) computer architecture. Computational theory also gets used (automata, properties of grammars).
 
Yeah, a programming class and the data structures class were my prerequisites for those classes.