32-bit and 64-bit OS:
A 64 bit processor is faster than a 32 bit processor. For 32 bits there is no need of any wide main bus to carry 32 bits at a time but for 64 bits its must that you should have a wider bus to carry 64bits.
On a 32-bit operating system, you are restricted to a maximum of 4 gigabytes of RAM. On a 64-bit operating system, you really do not have a limit. It can use 2^64 bits of space to address.
264 addresses, equivalent to approximately 17.2 billion gigabytes, 16.3 million terabytes, or 16 hexabytes of RAM.