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In general, yes, 64 bit processors do things faster. But it's a bit more complex -- 64 bit refers to the native word size of the processor, i.e. the size of the registers on the CPU. Therefore 64 bit processors can work on larger data and address more memory (32 bit processors being limited to 4 GB). But is a 300 MHz 64 bit UltraSPARC faster than a 3.2 GHz 32 bit Pentium 4? I don't think anyone would make that argument.
In addition modern 64 bit processors do incorporate some architectural improvements which helps them out.
it all depends, speaking from experience. Definitely is better if the stuff is compiled right. (Slamd64 is way faster at boot than 32 bit slack...on the same box)
but, some progs are optimized for say, multiple threads, instead of 64 bit. Everything feels a little bit beta-ey, but I think it's great. As far as over 32 bit, not if you use windoze, or most linuxes for that matter. Gentoo and Slamd64 linux are the ones that I've actually seen speed diffs in.
its not faster, as already stated 64-bit refers to how big of a number/data the processor can use, and also the adress's range, so 64-bit processes can use lots of RAM (without the needs for hacks to let the programs deal with more memory then they should have on a 32-bit address range)
the processor is still just as fast as a 32-bit one (at the same clock speed, and design), but improvements will be seen in performance for applications that can deal with big numbers (currently, if a application needs a 64-bit number on a 32-bit processor, the application takes longer as it splits the operation up into separate chunks to deal with the limited size in the processors registers, while in 64-bit processors, the registers are big enough to hold 64-bit numbers, so those are the applications that will see the biggest improvements.
all in all, 64-bit is better, but not worth the price if all you want is a descent computer that will suit most game needs, as well as average desktop use. if your one of those that wants a extra 1-3 fps on some game, then by all means, use 2 dual core 64-bit processors with 2 terabytes of RAM (that way, no need for swap, and you can preload most of your system), as well as a 1ghz GPU with 1 gig of fast on board memory connected to a AGPX10 slot, and a monitor with a latency of no more then 5ms. --- in the real world, just wait till prices drop, cause youl be upgrading in a few years anyways, right?
64 bits does not extend floating point as you may think (tell me if I'm wrong) because they're standard (IEEE-754). There's single precision (32 bits, C's float) and double precision (64 bits, C's double). With 64 bits processors, though, the FPU may easily use these, and casting between uint64_t and double would be easier / possible.