32 bit apps are designed for 32 bit processors and vice versa.
32 bit processor registers can only handle 32 bit (32 1s and 0s) operations per clock cycle. For integers this limits arithmetic between 0 and about 4 billion or 2^32. (Of course there are ways to calculate larger numbers by saving intermediary results into the DRAM, but that costs a lot of time)
64 bit processing increases this 4 billion limit of 32 bit processors to about 16 x 10^18.
32 bit will be backwards compatible on a 64 bit cpu because the 64 bit cpu has more computing “space” and can handle whatever 32 bit operations it needs.
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