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In theory, but some CPU don't scale as well with higher overclocks.

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Theoretically if you have 2 of the same CPU's, 1 at normal clock and the other at 2x the clock speed then yes I do believe you should have double the performance.

But in CPU land the comparisons rarely are that easy as you generally cannot overclock a CPU to double it's speed.

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100% depends on inner CPU architecture and RAM and/or chipset communication.

But, it's impossible to get 100% increase in performance from just doubling the clock speed.
Why ?
Because "Performance", is dependant on more than just pure clock speed.

EDIT :
Good example for how U can break this "simple clock gain math" theory is this :
U take something ridiculous (like Celeron D with GTX 780 Ti combo) and compare results from stock (ie. all AUTO settings - LINK), with OC'ed CPU/RAM - LINK (GPU clocks, OS, etc. are the same in both cases).

Stock settings in Fire Strike = 948pkt. : LINK,
OC'ed CPU (+67%) and RAM (+61%) = 1830pkt. : LINK.
So... I gained +94% in "pure CPU performance" (ie. Physics test), by OC'ing both RAM and CPU, by little over 60% :).
Of course, scaling for overall result is perfect since GPU is REALLY hold back here.

Hope this helps illustrate what is wrong with simple clock gain theory.

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Barring any other bottleneck like RAM or within the architecture itself, theoretically yes. In real-world however, it's a definite maybe.

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My camera lens sees the present…

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It'd be hard to find a cpu that would still be stable at double its clock speed without disabling cores anyway. The 6700k stock speed is 4Ghz and the highest someone was able to get it was about 7.1 or 7.2 and that's after limiting it to one core and running 4gb of ram. So at 8Ghz, it'd probably suicide. 

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yes your CPU will be capable of doing twice as much

but it doesn't  mean that your program will work twice as fast

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2 minutes ago, Sanderman135 said:

It'd be hard to find a cpu that would still be stable at double its clock speed without disabling cores anyway. The 6700k stock speed is 4Ghz and the highest someone was able to get it was about 7.1 or 7.2 and that's after limiting it to one core and running 4gb of ram. So at 8Ghz, it'd probably suicide. 

you can run the same cpu at 2GHz as well

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Well , there are multiple factors to consider , like cache , etc. I remember the early athlon chips having two cache pools running at half the speed of the cpu. That would mean that the more you overclocked , the less gain you would get.

For more recent cpus though , memory and cache bottlenecks aside , if you double the number of cycles , since the IPC doesn't change , the actual work done doubles.

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43 minutes ago, Sanderman135 said:

why would you do such a thing to a 6700k?!

I guess in this case it would only serve as an experiment 

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There is the potential for that to happen, but you could be held back by other things like cache quantity and bandwidth, or RAM bandwidth/latency, etc.  So, in theory, it could double performance, but you probably won't see a perfect scaling in many if any applications.

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