Hm... Good point. Though 'not there isn't really a state, but you could add as many zeroes as necessary in front, even though it's highly unusual (1010 is as correct as 0001010 in theory, no?)
Since we're limited to whole numbers, how efficient would be asking for divisibility? Is it divisible by 2 / 3/ 4... Skipping obviously wrong questions. (which is mostly just a way to get the binary approach to normal numbers) Is it much worse than other techniques?