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Binary
(i.imgur.com)
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Yep, I think the problem with most folks is that base 10 is taken for granted without fully understanding it. Maybe some of the concepts would be even easier to explain in hex instead of in binary - that you count to F instead of to 9 before flipping to 10, then explaining that binary follows the same principle, but only has two digits, hence has to flip to 10 sooner.