Windows 7 on a 64-bit computer

I read on Wikipedia that Windows 7 on a 64-bit PC needs twice as much RAM as on a 32-bit PC.
I understand why is that: every number stored in memory takes 8 bytes rather than just 4.
That, in simple terms, means that your amount of RAM is reduced to half when you use Windows 7 on a 64-bit computer.

Now, I have a Intel Core 2 Duo Laptop with Windows Vista right now (2 GB of RAM).
My question is:
Since Core 2 is a 64-bit architecture, if I upgrade to Windows 7 will my laptop be working as if it had just 1 GB of RAM?

Or... to say it in other words:
Having a 64-bit PC with Windows 7 do you need twice as much RAM as you need on a 32-bit PC to have the same performance?

If I am right, then I'd say it's a terrible business to have a 64-bit computer and Windows 7 on it (I hope I am mistaken, though).

Follow-up:
After some answers, I'm realizing it's not the same thing to have a 32-bit OS on a 64-bit PC than a 64-bit OS on a 64-bit PC.

Apparently, the problem of Windows 7 requiring twice as much RAM on 64-bit architectures is when you have both the OS and PC supporting 64 bits.
I'd like new answers to address this issue.
Also, is it possible to have more that 4 GB of RAM on a 64-bit PC using a 32-bit version of Windows?

Solution 1:

That is a terrible misunderstanding. Yes, your applications might take up a little more RAM, but overall, it will hardly be noticeable; they certainly won't take up twice as much memory. No one would switch to 64-bit if that was the case.

You'll be completely fine with 2GB of RAM on a 64-bit Windows 7 machine.

Per your followup: I don't know where you heard this rumor about Windows 7 taking up twice as much memory, but it's completely false. There is absolutely no way for a 64-bit OS to take up twice as much memory as a 32-bit OS. It doesn't matter what hardware you have on your computer.

The main advantage to having a 64-bit OS is the ability to use more than 4GB RAM. On top of that, any applications written specifically to take advantage of 64-bit processors are going to be slightly faster than their 32-bit counterparts. Other than that, there is really no major difference between the two. So I would say you probably don't need a 64-bit OS, although I would still recommend installing it because there's no reason not to.

Solution 2:

Only pointers use the double amount of RAM. All other memory content is the same as it was. And pointers make for just small fraction of memory usage.

However, with only 2 GB of RAM, you better have some other reason to want 64-bit. You almost get no benefits of 64-bit OS with that amount of RAM. The only two scenarios I can think of where 64-bit is required are Hyper-V (which will not be happy with RAM) and need to test something.

I would either upgrade RAM or stay with 32-bit.