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What exactly are the implications? Can a 32 bit linux run applications that are compiled as 64 bit? Or vice versa?

I just got a new machine with an i5 processor, I installed a copy of Ubuntu 10.10 which seems to be i686 which I new realize is 32 bit, but I think I have some 64 bit apps installed. Can this be right?

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You may also be interested in My processor is 64-bit - does that mean I need the amd64 image? and numerous threads on Super User. –  Gilles Jan 26 '11 at 19:38
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up vote 4 down vote accepted

You need a 64bit Operating System to run applications compiled for 64bit systems. You will, however, be able to run 32bit applications as well. It just doesn't work the other way around.

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That's true of Linux, but not of all OSes, e.g. OpenBSD amd64 can't run i386 binaries, and Solaris amd64/i386 can run both kinds of binaries on either kernel architecture. –  Gilles Jan 26 '11 at 0:56
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Exactly, but the question explicitly mentions Linux. –  lmontrieux Jan 26 '11 at 10:20
    
You MIGHT be able to run 32bit applications. It depends. Ubuntu is really good at including 32bit libs so I've never had a problem. But something like arch, getting 32 bit shared libraries on a 64 bit system isn't trivial. However if the binary doesn't have dynamic library dependences you should be fine. Unless you're building it from source. –  Falmarri Jan 26 '11 at 18:13
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