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Chip Composition of Memory Modules
Better quality SIMMs/DIMMs generally speaking use fewer, higher-capacity DRAM chips. Cheaper modules generally use more, lower-capacity DRAM chips, because older technology costs less. Since SIMM sockets are close together, using modules with many chips makes it harder for them to cool. This is especially true of double-sided SIMMs. Also, more chips means more of an electrical load on the motherboard.
Cheap 8 MB SIMMs are often made with 16 4Mbit DRAMs. Many lower-quality motherboards will croak if you try to put 4 of these SIMMs in them, because they can't handle driving 64 individual DRAM chips. (They almost never mention this in the manual, either.) Some 64 MB SIMMs are made with 36 DRAMs a piece--try getting 4 of those to work on a motherboard! In addition, many SIMMs with tons of chips on them (24 or more) are composite, and these present other problems for many motherboards.
Despite the fact that better modules use fewer chips, some older motherboards can have problems with them. In particular, some older PCs that use 30-pin parity SIMMs will not work with 3-chip versions. This has to do with the additional complexity of using different-sized DRAMs on the same SIMM: a 9-chip 30-pin SIMM uses 9 chips each 1 Mbit in size, but a 3-chip SIMM uses two 4-Mbit chips and one 1-Mbit chip. The motherboard manual may say if 3-chip SIMMs will work (or you may find that your system is already using them). If unsure, use the 9-chip SIMMs; 9 isn't a large number of chips for a SIMM in any event.
This table shows the typical chip composition of non-parity 30-pin and 72-pin SIMMs, which are usually found in 2, 4, 8, 16 or 32 chip configurations. Note that some of these are more commonly found than others, and that there are also other combinations that can exist. Manufacturers will tend to use whatever chips they can buy economically that will make up the right blend of depth and width; in particular for many SIMMs there isn't much difference between a 4Mx4 and a 1Mx16 for example, so there may be several different ways to set up the larger modules:
Here is the same table for parity or ECC SIMMs, usually found as 3, 9, 12, 18, 24 or even 36 chip modules: