Clarification: In the example with 0, 1, and 2 as allowed digits, I still intended for the number to be "binary" in the sense that the ith digit has weight 2^i.

Clarification: In the example with 0, 1, and 2 as allowed digits, I still intended for the number to be "binary" in the sense that the ith digit has weight 2^i. Thus, 12 in this system is 12^1 + 22^0 = 4, in decimal, and, in this system, 12 = 20 = 100.