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I have a question about the details of microprogramming and hard wiring in CPU architecture.

in hardwiring, we write a code the compiler translates it to the ISA. then ISA is run in the hardware.

in microprogramming, we write a code the compiler translates it to the ISA(which is much more complicated than the ISA in hardwiring)then a device(I don't know the name) translates it to the hardware language.

am I correct?

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Not Exactly. The microcode is a layer "below" the ISA and the Hardware-level functionality. That is, when you write some machine code like MOV or ADD or MUL (which are part of the ISA), the microcode translates it into multiple simpler activities (e.g., "move info from A register to B register. ADD this registers. Load from the Memory. etc.). These simple activities eventually perform the instruction you coded.

For instance, think of the MUL instruction that can be micro-coded as multiple add and subtract, like in done in elementary school.

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