Processor differences

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processor bits (32 v 64) are used to address memory.

a 32bit processor can address 2^32 (2 raised to the 32nd power)
this would be an address of 2,170 meg or also represented by
a hex number of ffffff

a 64bit processor can address 2^64 which is just plain B I G:) and
would be ffffff,ffffff

So your question really asks, "what kinds of applications use/need large
memory spaces"?
Typically these are big number crunchers, graphic image processes, and large DBMS systems

The OS itself can also benefit, but the motivation has always been to solve applications issues and then as the capability is present, why not exploit it to the full.
 
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