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Originally posted by Big Smoke
this isnt based on only what I know... This is written fact 
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I get what you are saying. But with the logic you present, the iPhone 5S would be slower than the iPhone 5. Obviously Apple have tweaked things, specially since the A7 is custom made.
Of course it doesn't have access to more memory. That's not what I'm saying. But a 64 bit processor, even on a PC with 2GB of RAM can still load information faster than a 32 bit processor.
If you look at Windows requirements, a 64 bit processor can see benefit on a computer with 2GB of RAM. Even though 32 bit can also run with 2GB.
But programs on a 64 bit processor (even with 2GB) will at least load 10% faster than 32 bit processor with the same amount of RAM installed.
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The visual I was taught in my course was, a 32 bit processor is like a boy in a library, trying to find a set number of books. The speed will help the boy go faster or slower in finding those books.
A 64 bit processor, will have several boys looking for those and of course they will find it quicker as each boy can look for a book rather than one boy look for them all.
This benefit of a 64 bit architecture is available to people with even 2GB (under the supposed 4GB or above only benefit). And on a phone with such a light OS, it's obviously seeing this benefit using 1GB (if you argue against this than the dramatic difference in speed in the 5S is unexplainable).
And of course, Quallcomm were saying it wouldn't work. Guess what they said after the scores came back?
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"The 64-bit Apple chip hit us in the gut. Not just us, but everyone, really. We were slack-jawed, and stunned, and unprepared,"
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They also went with the "not enough RAM, it's a gimmick" and they were very vocal about how they were wrong.