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Why is there a /usr/lib and a /usr/lib32 directory but only a /usr/bin and no /usr/bin32 directory on a AMD64 64-bit-install of Ubuntu? If or when Debian/Ubuntu start supporting multi-target-architecture binaries in their ELF's will this directory branching become unnecessary?

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Because it wouldn't be useful to install (for example) wget for amd64 and i386 on the same machine. One of them could be first in PATH, and so only that one would be executed when you ran wget.

Installing binaries from multiple libraries at the same time is only useful for shared libraries.

Oh, also, multiarch doesn't use /usr/lib32, that's a hack used in bi-arch (which we've never really done in Debian/Ubuntu). The multiarch libraries live in /usr/lib/x86_64-linux-gnu/ for amd64 and /usr/lib/i386-linux-gnu/ for i386.

You can find the name of that directory by running:

$ dpkg-architecture -qDEB_HOST_MULTIARCH
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