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You can count past 1,000 on your fingers by using binary, instead of just 10
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I like your way, learning as an adult.
But if you were to hypothetically teach a child, then binary would be easier, and they eventually would memorize the positions.
Although realistically by the time they need their second hand, they probably don't need to be counting on their fingers anymore. And I don't think either of these systems is especially helpful for higher math, unless you're multiplying or dividing by a power of 2. Maybe? I forget my 2s compliment operations now.