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A 32-bit OS has the chip (if it is 64-bit capable at all) operating in its 32-bit compatibility mode, and as such it cannot run 64-bit software.
The reverse, however, is not true. 32-bit application software can be run by a 64-bit operating system, which puts the processor into (user-mode) compatibility mode for the duration of running that particular process.
And nevertheless: what you should do, as soon as possible, is to upgrade that software. 64-bit software is capable of addressing far more memory than 32-bit applications can, and this is a big differential in terms of runtime speed and capacity.
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