32 bit processors / 64 bit processors

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Hi,

Firstly, I'm trying to understand what exactly characterizes a
procesor or an operating system as 32bit / 64 bit. I've read that it
means the "native word size" of a machine. But what exactly is that?
Register size? Address bus size? Anything else?

Secondly, I'm trying to understand what exactly does a sizeof(int)
depend on when we say it is "platform specific". Is it dependent of
compiler being 32bit / 64 bit? Or the OS being 32bit / 64 bit? Or the
processor being 32 / 64 bit?

Lastly, How are "sizes" of compiler / OS / processor inter related?
Here is my understanding. A 32 bit processor can only be running a 32
bit OS. A 64 bit processor may run a 32 or a 64 bit OS. A 32 bit
compiler genrates code only to be run on a 32 bit OS; ditto for 64
bit. Is this right?

TIA,

Rick
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