Benefits of 64 bit over 32 bit when writing software

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If I have a simple program written in C++ like HelloWorld, and then I compile it in a machine of 32 bit and 64 bit, I get two different binaries doing the same but they are different machine code and only 32 bit binary will be able to run on 32 or 64 bit machine.

In both case I don't have any benefits because the source code is the same and they do the same. This makes me to think the all software packages of some Linux distro written for 32 bit could be ported to 64 bit machine without to do anything change. Then, what do I get ? Any benefits?

Is there any example of code in C/C++ that I can do some in 64-bit that I can't do in 32-bit ?

For example, Google Chrome right now is unsupported in 32 bit, but not in 64 bit. Which could be the reason?

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