SDRAM is designed to synchronise itself with the timing of the CPU. SDRAM has a SPD (Serial Presence Detect) chip for the motherboard to detect the timings of the SDRAM module. PC100 and PC133 memory have different timings on their respective SPD chips. This would make PC100 and PC133 incompatible. However the timings are very similar and they have been known to work together.

512mb PC133 DIMMs are only 100% compatible in motherboards with Pentium 4 processors.
If your motherboard specifications state that it can use 512mb DIMMs but the system has a slower than P4 processor, there is a low chance of compatibility.

No. The SPD chip contains only the timing information for a PC133 module. The timing information for PC100 and PC66 is different. However PC100 timing is similar to PC133 and customers have found that PC133 memory work in PC100 systems.

SDRAM is designed to synchronise itself with the timing of the CPU. SDRAM has a SPD (Serial Presence Detect) chip for the motherboard to detect the timings of the SDRAM module. PC100 and PC66 memory has different timings on their respective SPD chips. Therefore they are not compatible.

There are various ways to make a 256mb PC133 modules. The to common ways are: 16chip DIMMs using 16x8 chips and 8 chip DIMMs using 32x8 chips.
The 16 chip 256mb DIMMs are the most compatible as it is the original, and hence recognised by most motherboards using PC133 modules. The cheaper 256mb modules are 8 chip using 32x8 chips. This is the same chip used to make 512mb modules. The 256mb 8 chip module has the same compatibility issues as the 512mb PC133 DIMM.

PC100 SDRAM is memory designed for the 100mhz bus motherboards and CPUs. SDRAM up till this time were designed to work in the 66mhz bus. To ensure modules were compatible, Intel introduced an industry specification termed PC100 compliant. All Upgradeable.com PC100 100mhz SDRAM is PC100 compliant.

PC133 133MHz is an enhancement to the original specification for PC100 100MHz memory modules.

SDRAM is an abbreviation for Synchronous DRAM. It is designed to synchronise itself to the CPU timing. Unlike asynchronous DRAM (FPM/EDO), SDRAM has a clock input, so the system clock can control the SDRAM operations. It frees the processor from waiting between memory accesses. SDRAM can operate up to four times the rate of conventional EDO DRAM.

The 512mb PC133 DIMMs were probably released after the manufacture date of your motherboard. Basically the motherboard does not know they exist. Some motherboard manufacturers allow for the introduction of higher capacity DIMMs but fail to release BIOS updates. Check the manufacturer's website for a BIOS update that allows the installation of 512mb modules.

The Upgradeable 256mb PC133 modules are 16chip DIMMs using 16x8 chips. The 16 chip 256mb DIMMs are compatible in all motherboards using PC133 modules. The cheaper 256mb modules are 8 chip using 32x8 chips. This is the same chip used to make 512mb modules. The 256mb 8 chip module has the same compatibility issues as the 512mb PC133 DIMM.