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What you say is correct except for the very last part which is inaccurate. C works with word-addressed CPUs (I can see one from here, and it has a C compiler. And was, incidentally, sold into the early nineties). What C needs is a way to work with 8-bit characters, that's all (and even that isn't 100% true, just widely expected). So what a C compiler needs on, say, a 16-bit addressable computer, is a way to access a char, an 8-bit entity (everything else, e.g. int, long etc., is up to the architecture). And that can be done by software, or more typically by the CPU having opcodes to access 8-bit fields within its native addressable word size.

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