64-bit Kernel Running 32-bit ELF Executables – How It Works

You can use the file command to check out what format the executable file has.

eg:

$ file /bin/bash
/bin/bash: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.9, stripped

A 32-bit process can access only about 3GB. (It can be less, depending on the kernel compilation options.) It doesn't matter whether the kernel is a 32-bit or 64-bit one — that only affects the ability to run 64-bit applications. PAE is a way to allow more physical memory but doesn't change the size of the virtual memory seen by each process. That's pretty much what “32-bit” means: a pointer uses 32 bits, so there are only 2³² possible virtual addresses, so each process can access at most 2³²B = 4GB. Linux reserves 1GB for kernel use during system calls, which leaves 3GB.

An application can use more memory if it runs multiple processes.