All 32 bit Windows desktop editions newer than "Windows XP SP1" are unable to access any memory above 4 GB. This is a license limitation of all 32 bit desktop editions. Server editions have other limits.
For compatibility reasons some memory below 4 GB will be reserved for hardware and not usable. The BIOS will remap this memory above 4 GB.
In your situation you will have the following memory layout:
0.00-2.75 GB: RAM
2.75-4.00 GB: reserved for hardware
4.00-7.25 GB: RAM
So you still could use the full 6 GB of RAM. But the license restriction will just cut off everything above 4 GB, so you will only be able to use 2.75 GB RAM. The registry key storing the LicensedMemory information is protected, you cannot bypass the limit without patching system files. These patched files could be overwritten every time you update your OS or do an error check.
Every normal 32 bit program will run on a 64 bit OS without any restrictions or speed penality. The only expection are device drivers.
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