As you can see from the dmesg output, the kernel sees 1047488k of
memory, that is ~1023 MB (just like any other operating system sees on
your system).

Now on Linux, some of these 1023 MB are reserved and used by the kernel.
So the total memory available and visible (!) to applications becomes
1023 MB minus whatever the kernel reserves; apparently that makes 1003
MB in your case. Windows showing other numbers is merely a difference in
accounting, as Matthew Garrett already pointed out.

-- 
Ubuntu Does Not See All My Memory
https://launchpad.net/bugs/87957

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