I was thinking about the different number systems, and realised that technically binary is not the simplest. The simplest is unary - i.e. powers of 1. Wikipedia confirms this view: https://en.wikipedia.org/wiki/Unary_numeral_system
I was wondering what the representation of a number would look like in this system and it seems to be a tally format.
However, this system does not seem to fit the pattern we see in other bases. Decimal requires 10 different symbols (if you include 0), nonary requires 9, down to binary which requires 2. Surely then unary should require 1 by following this pattern through. You could argue it does, and that unary has its equivalent in a tally system. However, by including the symbol 1, do we not implicitly imply the existence of the symbol 0? If there is something, then surely its absence implies nothing? This would mean of course that both binary and unary require two symbols to represent them.
Even if you argue that decimal only really requires 9 symbols, with 0 being implied by the absence of a symbol. In this case, how could we possibly represent a number in unary with no symbol other than the implied 0?