>I imagine that it's because in the binary system, 11 only equals decimal 3 because 2^0 + 2^1 = 3. Otherwise, you'd have 2^1 + 2^2 = 6. If the 1st position isn't '0', then how would you represent decimal '1' in the binary system?

While internally it is like that, if, in .NET for example, some items are one based as oppose to zero based, I assume that, on the other end, they could have made all of them available either as zero based or one based but not a mix of both.