If you're mapping datatypes, or dealing with bit arrays.

The root of the problem, which manifests itself in scenarios far more often than you might think, is that in big endian, the location corresponding to 2**n within an integer maps to byte X - n/8 - 1, where X is the number of bytes in the mapped-to data structure, and if it's true big-endian like some IBM processors, the bit maps to bit number 7 - (n%8), but with most processors which are mixed endian, such as the M68K, it's merely n%8.

With little endian, the byte location is n/8 and the bit location is n%8.

A trite example of when this occurs is that you have a description of bit numbers within 4-byte hardware registers and you want to develop an integer mask for those.