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CPU's
CPU technology is advancing at an amazing rate, for those just wanting a PC to browse the internet and use basic office software then a Pentium D or AMD Athlon dual core is ideal, the minimum should be a a Pentium D dual core at 3.2Ghz or a AMD Athlon Dual Core 3800 or above.
For those wishing to run more complex application and undertake digital photography / video editing then a higher spec CPU is essential if you want the PC to perform at a reasonable speed. In terms of what's available today, the Intel Core 2 Duo E6300 or above are very good processors, if you prefer AMD then go for the AMD Athlon 64 X2 6000+ although bear in mind that this processor is the last of the current series from AMD and will be replaced towards the end of 2007.
For Laptops, I would recommend Intel Core Duo T2300 and above.
If your looking to the future and are likely to keep your computer for more than 3 years then it might be worth considering a Quad Core CPU, in short this is four processors in one as the name suggests! Currrently these processors are primarily available for Desktop PC's however I would expect this to change over the coming months
On today's applications the current set of Quad Core processors are slightly behind the fastet Duo Core CPU's, however as applications become more complex the ability for your CPU to multi-task will become more important. A good example of a Quad Core CPU is Intel Core 2 QUAD 6600.
Always try and buy the best CPU that you can afford when looking for a new Computer, other components are easier to upgrade e.g. memory, graphics, hard drive but a CPU upgrade takes a little more knowledge and expertise to get it right.
CPU's are generally the most expensive component of any computer so you want your new computer to have a CPU that will still be able to comfortably manage the applications that you may want to use in 2008, 2009 and beyond.
Overclocking
It is possible to increase your performance of your CPU by a process of overclocking whereby you increase the speed that the CPU will operate at by amending other factors such as voltage. Unless you are very competent and/or very brave I would not attempt this! The best case is that your PC will run a little quicker but you will be hard pressed to tell the difference unless you are running benchmark scores, worst case is that your CPU dies and you need a new one along with anything else that has been damaged!