Can you have 64-bit programs on 32-bit os with 64-bit processor?
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You can't run 64 bit's program on 32(x86) bit even with 64 bit processor.
You do need to install OS of 64 bit to run a 64 bit's program.
There are some difference between 32 bit and 64 bit OS
they're commonly known as architecture of machine.
32 bit OS or processors process less instructions.
A 32-bit system can access 2^32 memory addresses
Whereas a 64 bit can access 2^64 memory addresses
Machines made in early 1900 and 2000 deals with 32 bit system.
Now a days, 64 bit is common.
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