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c++ - how does assembler convert from assembly to machine code?

I know this has been asked many times, but I am looking for a simple interpretation.

Let's say I have some assembly code that C++ compiler generated.

Now assembler kicks in and it has to transform the assembly code into machine code.

Question 1). Will the C++ assembler compiler look at the table where each assembly instruction has the corresponding machine code instruction ?

Question 2). If the C++ program runs on the intel processor, then, assembler needs to take a look at the table published by Intel team, right ? because in the end, C++ program runs on the intel processor.

Question 3). If I am right about the question 2, then how is it possible that program written in C++ can be run on the computer which uses Intel and on the computer which uses AMD processor ?

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