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You're really asking two questions, let me tackle them in opposite order.

One of your questions is about clock speed. Clock speed is the amount of cycles a processor can complete per second. Clock speeds between processors are NOT comparable unless the processors are of the same family (IE. all Bulldozer AMD processors have clock speeds that can be compared, all Intel Ivy Bridge processors have clock speeds that can be compared, but you cannot compare Bulldozer and Ivy Bridge clock speeds).

The reason clock speeds are NOT comparable to each other is because the number of instructions that are completed per cycle is different. The number of instructions completed is inversly proportional to the size of the core (the smaller physical distance the eletrical signals have to travel, the more instructions can be completed per cycle).

Intel Ivy Bridge uses 22nm processes and is the "fastest" clock speed currently on the market. Intel Sandy Bridge comes in second using a 32nm process. AMD's and 1st generation Core i Intels use 45nm processes and are the "slowest."

On to your second question, how do cores effect the productivity of a processor:

EDIT: (It's REALLY important to note: extra cores are ONLY utilized if the SOFTWARE is written to use them. Processors DO NOT split their work loads unless the APPLICATION tells them to. Utilization of multiple cores is SOFTWARE DEPENDENT, the processor will NOT do it on it's own).

The clock speed of your processor is NOT the clock speed multiplied by the cores. Each core runs at whatever clock speed is listed. For example, a quad core Core i5 or Bulldozer running a 2.5Ghz will have 4 cores, and each core has a clock speed of 2.5Ghz (2.5 giga-cycles completed per second).

If an application on your computer is written to utilize multiple cores, then it will take advantage of 2, 3, 4, or up to 8 cores (depending on your processor, and how many cores the application is written to use) on your processor, and be able to complete it's work load faster.

PC games typically use 2 cores, 1 for sound, and 1 for everything else. Some games are written to utilize more cores, the Battlefield series is pretty good (not perfect) at utilizing multiple cores. When I played BFBC2 on my Core i7 (4 physical cores, with hyperthreading it was able to actually utilize 8 instructions at the same time) I typically saw between 3 and 5 threads (cores) being utilized. But Battlefield is the EXCEPTION, 99% of games will only utilize 1 or 2 cores.

Applications like Adobe Premier (designed to let you edit video, and compile video) are written to utilize multiple cores - Adobe Premier on my Core i7 used all 8 threads.

So, the answer to how many cores is better/faster depends on the application you're using. In most games, with no background applications, a dual core will perform the same as an octa-core assuming their clock speeds and instructions per cycle are the same. Throw in a few background tasks and you might see increased performance in a quad core, but beyond that you won't get any benefit.

In fact, the i5-2500K (a 4 core, no hyperthreading processor) typically outperformed an i7-2600K (4 cores, hyperthreading to utilize 8 threads, or 4 extra "virtual" cores) in games because of better use of the processor's cache and turbo boost.

You should always buy a processor designed for the task at hand, not only can more be over kill, it can actually hurt your performance.

1) No, that just means you have 4 cores working at 2.2 ghz. The work that the computer does is distributed across all cores, so each core is doing less work making it faster.

2) It depends what you are doing, if you are running multiple applications at once then the quadcore is faster for sure, but if you are just doing a one or two things he 3.0 is faster

3) the 3.0 Quadcore is much faster, like I said above you have 4 cores each running at 3.0 Ghz

Having multiple processors doesn't make the speed go up, but it handles workload more efficiently. Say if you have a program that utilizes multi-core processors, but ran it on a single core processor, all the work load would be on that single processor rather than being spread out on multiple processors. You could only run a few programs on a single processor whereas a multi-core processor you could run a dozen programs, a game, and surfing the internet all at the same time, without any hiccups.

Quad-core processors will always be faster and more efficient to handle workload than a single processor regardless of how fast it is.

1) Yes and no. It's not as simple as multiplying it together and adding it up - the CPU will not always be using all 4 cores at the same time, so in practice, you will never get 4x greater speeds.

2) 2.2GHz quad core. Also note that the 2.2GHz quad core processor is also likely to have other better specifications (high cache memory, other technologies) and also likely to be from a newer generation, increasing performance.

3) 3GHz quad core of course.

I like Joseph answer..he has it down pretty well. simply put you don't multiply individual core speed.

IF a program can use more cores then you have a better advantage with more cores. Each core can do more work solving a problem than one core trying to solve the whole problem.

A 3.0GHz processor is 3.0GHz regardless of how many cores.

The more cores, the more processing power