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I have a relatively clean installation of Ubuntu which reads this under system details:

details

I've read everywhere that 32-bit OSs don't support more than 4 GB of RAM (some sources say 3 GB), so what's going on in my system? Does it recognize but not use all the RAM I'm providing it (BTW, the System Monitor also shows 5,8 GiB) or what? Unless the system installed PAE automatically, I'm not using it. I've taken a look at the answers on Does Ubuntu Desktop 32Bit Support more than 4GB Memory with default installation?, but am still looking for an answer to my case.

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If it's showing that, you're probably using PAE. It's enabled by default.

Why is it 5.8GB instead of 6GB? Do you have onboard graphics? It's probably reserving a chunk.

Oli
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The sentence "32-bit operating systems don't support more than 4 GB of RAM" is false in general. The Physical Address Extension, which is CPU feature, allows the 32-bit operating system to address more than 4GB of RAM. It is true, however, that some editions of 32-bit Microsoft Windows system don't use Physical Address Extension due to marketing reasons and hence don't support more than 4GB of RAM. The myth of only 4GB of RAM in 32-bit systems have grown on popularity of such Windows editions.

32-bit Ubuntu makes use of Physical Address Extension, so you can use more than 4GB of RAM in your 32-bit system.