In the computer world, 32-bit and 64-bit refer to the type of central processing unit (CPU), operating system, driver, and more that utilizes that particular architecture.
You will have seen the option to download a piece of software as a 32 or 64 Bit version and the difference does in fact matter because the two were programmed for completely separate systems.
32-bit systems utilize data in 32-bit pieces while 64-bit systems utilize data in 64-bit pieces. In general, the more data that can be processed at once, the faster the system can operate.
There are several other reasons to use a 64-bit system as well, most practically the ability to use significantly greater amounts of physical memory (more than the 4 GB allowed by a 32-bit machine).
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