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Output of uname -a on my RHEL 5.4 machine is:

Linux <machine name> 2.6.18-164.el5 #1 SMP Tue Aug 18 15:51:48 EDT 2009 x86_64 x86_64 x86_64 GNU/Linux

Does it mean that hardware is 64 bit (going by perhaps first x86_64) and OS is also 64-bit going by last x86_64?

Also, what are these so many instances of x86_64?
Can I install 64-bit vm over 32-bit OS and vice versa?

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The hardware, the kernel and the user space programs may have different word sizes¹.

  • You can see whether the CPU is 64-bit, 32-bit, or capable of both by checking the flags line in /proc/cpuinfo. You have to know the possible flags on your architecture family. For example, on i386/amd64 platforms, the lm flag identifies amd64-capable CPUs (CPUs that don't have that flag are i386-only).

    grep -q '^flags *:.*\blm\b' /proc/cpuinfo    # Assuming a PC
    
  • You can see whether the kernel is 32-bit or 64-bit by querying the architecture with uname -m. For example, i[3456]86 are 32-bit while x86_64 is 64-bit. Note that on several architectures, a 64-bit kernel can run 32-bit userland programs, so even if the uname -m shows a 64-bit kernel, there is no guarantee that 64-bit libraries will be available.

    [ "$(uname -m)" = "x86_64" ]    # Assuming a PC
    
  • You can see what is available in userland by querying the LSB support with the lsb_release command. More precisely, lsb-release -s prints a :-separated list of supported LSB features. Each feature has the form module-*version*-architecture. For example, availability of an ix86 C library is indicated by core-2.0-ia32, while core-2.0-amd64 is the analog for amd64. Not every distribution declares all the available LSB modules though, so more may be available than is detectable in this way.

  • You can find out the preferred word size for development (assuming a C compiler is available) by compiling a 5-line C program that prints sizeof(void*) or sizeof(size_t). You can obtain the same information in a slightly less reliable way²

As for virtual machines, whether you can run a 64-bit VM on a 32-bit system or vice versa depends on your virtual machine technology. See in particular How can I install a 64bit Linux virtual machine on a 32bit Linux?

¹ “Word size” is the usual name for what you call bitness.
² It can be unreliable if someone installed an alternate C compiler with a different target architecture but kept the system default getconf.

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Have a look at man uname.

You can compile and run 32-bit programs on a 64-bit machine (though this requires a special setup), but can't run 64-bit binaries on a 32-bit system. Same applies to many Virtual Machines, but not all*. So if you have a 64bit kernel, there's no way that your hardware is 32-bit-only.

If you want to test for what bitness a binary program is made, run file /path/to/the/program.

* This depends on the level, on which a given Virtual Machine operates: Those that execute binary code (almost) directly on the host CPU, will not be able to run 64-bit code on a 32-bit host. Those that emulate a certain CPU can do it, but they are less efficient because of the emulation level.

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You can compile 64bit binaries on 32bit systems, just not run them. And 32bit VM could emulate a 64bit CPU. –  Mat Nov 16 '11 at 13:30
    
Good point about compiling - my bad. The second part depends on the VM software, IIRC. –  rozcietrzewiacz Nov 16 '11 at 13:38
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Some VM packages can run 64-bit guest OSes (and 64-bit software within them) natively on a 64-bit CPU, even if the host OS is 32-bits. –  David Schwartz Nov 16 '11 at 20:30
    
@DavidS Good point as well... Still, no way that could be done on a 32-bit CPU. –  rozcietrzewiacz Nov 16 '11 at 20:48
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