This is pretty interesting, but I'm missing something. Intuitively, your digit-wise MIN description of 'AND' makes sense to me. But your examples don't work when using two's complement encoded versions of them. 124 & 310 == 52 right? Help me connect the dots.
See it this way: Numbers are distinct from their representations. 0x10, 0o20, 16 and 0b10000 are four different representations of the same number. The & operator doesn't operate on _numbers_, it operates on their binary representation — in many ways, it's almost like string manipulation.
What I suggested was that that way of operating on the representation of the number would work on any base in a way that is consistent (but, importantly, doesn't yield the same numerical result!) with the binary version.
