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32-bit vs. 64-bit systems
I know that there are 2 types of OSs, 64 bit and 32 bit What is the main differences between them?
And if I am buying a new laptop, which one should i install?
It will be able to run all applications if I installed either of them?
I am talking mainly about windows Operating systems, but you can answer about others as well.
mainly the amount of RAM accessible. In most 32bit OSs there is a 4gb (closer to 3gb actually) ceiling. I believe vista x64 can access up to 128gb.
Realistically, unless you're a power user it won't matter. Very few activities you'd do on a daily basis will require more than 3gb of memory. Also, driver support for 32bit OSs is slightly better.
64bit apps will not run in a 32bit environment. However, you probably won't find very many apps that are exclusively 64bit. 32bit apps will run fine 99% of the time in x64.
The bottom line is that there probably isn't a perceptible difference for most end users, but 64-bit is the wave of the future (present?) and does offer significant improvements. You'll be able to run lots of apps concurrently with either 32-bit or 64-bit, but with the 64-bit and lots of RAM, performance will be better.
The previous answers have correctly stated that the amount of usable RAM ("addressable memory" in nerd-speak) is a key difference between 32-bit and 64-bit. It should be obvious that your can only run 64-bit code on a 64-bit processor. However, even an OS that is not "fully" 64-bit can run 64-bit processes. For example, OS X has added 64-bit support in stages with 10.4 and 10.5, and now 10.6 ("Snow Leopard") pretty much everything from the kernel to the included applications are 64-bit.
As far as classifying operating systems based on 32/64-bit, it's actually somewhat of a false dichotomy. Windows ships separate 32/64-bit versions, but (for example) OS X ships as a single OS that can run in either mode. The reason Apple can do this is because they invested in Rosetta and also developed and promoted universal binaries. At first this was to make the PowerPC → Intel transition work, but now they can also leverage the technology to bundle 32/64-bit binaries in the same application, and the OS can choose which to launch as necessary. Windows support is likely to be somewhat different.
The vastly increased memory limits aren't really that important to end users (at least not now), but are critical for high-performance and memory-intensive applications. Even so, if a 64-bit machine and OS work for you, it's smart to buy with an eye to the future, because that's where computing is headed.
(Disclaimer: Nerdy details follow...)
One low-level but important detail that has been left out is that the 64-bit Intel (nee AMD) architecture (aka "x86_64") has a different CPU structure that adds some efficiency over the 32-bit architecture. There are twice as many "program registers", which is basically wicked fast memory that the CPU can use to cache information, resulting in a performance gain. Also, 64-bit code and language runtimes can discard years of backward compatibility with 32-bit cruft and make some new optimizations to code and execution pipelining that were previously impossible, and ongoing compiler development will continue to increase the gap.
Edit: See this AppleInsider.com post now that Snow Leopard has been released: http://www.appleinsider.com/articles/09/09/02/inside_mac_os_x_snow_leopard_64_bits.html
32 bit vs 64 bit refers to the address space, and as others mentioned this translates into the amount of RAM you can use: 32 bit = 4GB, 64bit has a theoretical ceiling of 16, 384 petabytes. Wow.
The fact that you are posting on superuser probably indicates that you aren't a "normal" user. If all you're doing is checking email and writing word docs, you are probably ok with 32-bit; however, if you are buying a new computer and you're not looking for a cheap netbook, I see no real valid reason NOT to go with a 64-bit system. There are, however, many reason to get a 64-bit and thus as much RAM as you can get your grubby hands on, including : compilation performance if you're a programmer, multitasking performance, heavy duty video/graphical editing performance, VM performance, and high-end gaming performance. Notice the keyword performance? If that is important to you in the future, go for 64-bit.
32 and 64 are references to the word size, or basically, how many bits the CPU can work with at a time. It affects how instructions are composed, passed and manipulated.
The computer is able to reference a larger amount of memory due to this reason, as cited in other answers. If you can, you should go with the 64 bit system, although the most gains are seen in really CPU intensive work, such as video editing/processing.
The major difference for every day use is that 64-bit will allow more than 4GB of RAM. You should be able to run 32-bit applications on your laptop with a 64-bit OS too. Just like you can run 16-bit applications on your 32-bit OS.
-JFV
