I think I was about 8 when I was introduced to the concept of counting in binary, using an analogy from base-10 counting. We'd already done sums with carry so introducing base-2 wasn't so hard. I'd also seen the "Schoolhouse Rock" cartoon with base-12 counting, so it wasn't much of a reach.

Maybe hex would be easier ("What if we had 16 fingers instead of 10?")...