It's not the processor the determines the RAM type but the motherboard (mobo). Most older mobos use simms (single inline memory module). These need to be used in pairs. For instance, to get 16MB you would need to have two 8MB sticks or, if you have enought slots on the board, 4 4MB. Newer mobos use dimms (dual inline memory modules). These sticks do not have to be used in pairs. As far as I know you can not use one of each (it's been a while since I've seen a simm, but I think they fit into different shaped slots). Now, you also need to know at what speed RAM you need. For instance if you have a Celeron system, you need PC66 RAM that runs at 66MHz. If you have a Katami PIII (most PIII's below 600 I think) you would want PC100 RAM becuase that is the front side bus speed of the CPU. Of course, the mobo also has to support the FSB speed. If you have a Coppermine PIII (most PIII's above 600 I think) who's FSB runs at 133MHz but the board only runs at 100MHz, you will not be able to fully take advantage of the possible performance. In addition, there are other bus speeds ranging from 150 or so to 800. I'm sure other people can give you more info on AMD chips.
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