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Changing the multiplier on an Intel CPU is not an option so you will have to change the FSB. Some of the AMD CPUs will allow you to change the multiplier, you will have to check more about this on the AMD specific sites as to which ones can be changed and what you will have to do to allow it.
The other part of the equation is the FSB, formally known as the 'Bus Frequency'. This is relatively simple to change if you have a motherboard that will allow it. Most overclocker friendly boards have various steps of frequencies to allow you to gradually increase the speed of the CPU to be able to push it to its maximum speed.
Most overclocker friendly motherboards will jump to 75Mhz, then 83Mhz and most up to 90Mhz and higher. You must beware to keep track of what your PCI and AGP buses are running at. Some motherboards will automatically set these to the closest available speed to the normal specifications as possible. The PCI bus runs at 33Mhz and the AGP at 66Mhz. These speeds are calculated from the FSB by the AGP and PCI dividers. If we are using an FSB of 66Mhz, the PCI divider will be 1/2 and the AGP divider will be 1/1. (66Mhz x 1/2 = 33Mhz, 66Mhz x 1/1 = 66Mhz). If we increase the bus speed to 83Mhz for example, we now have a problem of trying to keep the AGP and PCI buses as close to their normal speeds as possible. For the PCI, 83Mhz x 1/2 = 41.5Mhz. This is a tad high for most PCI devices to handle. The AGP bus will also be running high, 83Mhz x 1/1 = 83Mhz. In most cases, a Celeron 600 will be able to handle jumping up to a 100Mhz FSB. This will allow you to use AGP and PCI dividers which will give you the exact specifications speeds for each bus, 100Mhz x 1/3 = 33Mhz (PCI), 100Mhz x 2/3 = 66Mhz(AGP). If you have a 100Mhz FSB already, then a slight increase will not be too severe. This also applies to a 133Mhz FSB CPU. Just try and keep each bus as close to specifications as possible. Using higher speed AGP and PCI bus speeds can cause problems with some devices.
The memory bus is also clocked off the FSB. Most boards will run the memory bus at the same speed as the FSB and there is no way of changing it. Some boards will allow you to alter the memory bus by + or 33Mhz. You will have to check the specifications of your board to see if it will allow this. If for example you are running your FSB at 100Mhz and want to bump your memory bus up to 133Mhz to take advantage of your PC133 memory, you can add 33Mhz to your FSB and run your memory at 133Mhz to give a slight performance boost. This is also true if you want to run your CPU at 133Mhz but only have PC100 memory, just subtract 33Mhz from the FSB and your memory will run at 100Mhz. This can also be handy to check and see if your memory is causing problems at high bus speeds or if it may be something else. You will of course want to run the memory as fast as possible also to give the most performance available. Running memory at too high of a speed can cause your computer to lock up. If for example you are using PC100 memory (designed for 100Mhz) and you are trying to run at 133Mhz, chances are your computer will not boot. Most memory can handle a little over what it is rated for. In general, PC100 can go to 110Mhz, and PC133 up to 140Mhz. To be safe side, get the highest quality memory you can, PC150 (or better) is highly recommended if you plan on doing overclocking. Minimum is PC133. The rules will change a little when we start using RDRAM and DDR.
The memory timings can also play a role in how well the memory will perform. Most boards will allow you to tweak the memory settings. When you begin overclocking, keep the memory settings at the slowest possible so you can put all your attention toward the CPU and then tweak the memory later on. There are alot of different BIOS's out there, so I can't tell you specifically what each setting will be, just remember that the higher the memory timing, the slower it will run. (CAS3 is slower than CAS2, 10ns is slower than 8ns)
If you begin overclocking and experience alot of instability, you will have to determine what may be causing the instability. In most cases, it will be the CPU causing problems. One way to help a CPU handle higher bus speeds is to increase the core voltage supplied to the CPU. This is determined by signals from the CPU to motherboard. Some boards will allow you to adjust the voltage a little bit, but others will not. You may have to use a few tricks in order to use a higher voltage. Basically, if you change the signals from the CPU to the motherboard, you can change the voltage. Instability is not always caused by the CPU though. It may a PCI or AGP card, or it could be the motherboard itself,some chipsets will not handle higher than normal bus speeds.
Overclocking is a trial and error process. Just because someone got their computer to run at a higher speed doesn't mean yours will run at the same exact speed. The best way to begin overclocking is read the reviews of various CPUs and Motherboards and decide which components will be the best match to allow you to maximize your overclocking potential.