I have a Compaq Pressario SR1222NX that I am looking to upgrade the RAM on. So the max supported RAM is for my computer is 4 GB. This makes sense to me as the 32 bit address limit is 4GB. However... According to intel, the chipset of my computer will support up to 8GB. So I dug around a little bit more and found This document from intel that specifies that "[8000MB] exceeds a 32-bit address limit of 4 GB. In a 32-bit system, only the first 4 GB of memory will be accessible". Apparently, all I have to do is install a 64bit OS. I am very doubtful of this as my computer has a 32bit Intel Pentium 4. So, I am wondering if the 8gb of ram will work in my computer without modifications, and if not, what modification would I have to make?
32 bit systems have supported more than 4 GB of RAM for well over a decade, through the use of PAE.
That said, the specs say that your computer's maximum supported memory capacity is 4 GB, so it's 4GB, and what the chipset supports doesn't much matter. It might be a BIOS limitation, it might be that the system board only supports a maximum DIMM size of 1GB, it might even be that the system is so old they hadn't considered the existence of larger DIMMs. Regardless, the better approach is to buy a new computer, rather than throwing money away upgrading this one. It's over 10 years old, FFS. That's beyond geriatric in computing terms. It's almost an antique.
The chipset supports some 64 bit chips, and if you had a 64 bit capable chip you certainly could. This chipset's around the time intel made the transition, and from checking a random sampling many of the chips it supports are 64 bit.
However at the time the system was released, 64 bit windows wasn't really a thing. I suspect most systems ran xp, and 64 bit support for XP was not too good.
That said, if its ddr2 some systems have issues with 2gb sticks, and you'd need 4 slots (so 4x2gb) to max it out IIRC.
So, it might work or it might not. However its a reasonable bet that if you have the slots, and the right type of ram, detected in the bios, and a 64 bit OS, it should work fine.