^32 limitation and modulo methods

In Java, Integers must be between 2^31 - 1 through -2^31 so if int x = 2 * 1500000000 The logical answer will be 300000000 but because it has a limit on its value, it is thus brought forward and using 2^32 mod 3000000000 it will be -1294967296 but because it is brought forward the number will become negative because the positive field is overflown. Am i right to say that this is true? Also, I have search and read up on the modulation part, for e.g. in a clock 15 mod 12 == 3 because it is the remainder of the division however it is good as an example for a clock because 12 is a constant here. So is 2^32 is the constant of all modulation computation of integers for overflow?
 
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