Learning long operations with tokens is easier in many ways. For example, the adding app, which you just tried, uses only two numbers and builds the result on top of one of them. It doesn't rely on any knowledge of "math facts," and it handles overflows immediately. Without deferred carries, one can instantly see how much is left to add, and what we are going to add it to. Best of all, this algorithm is reversible. It's equally good for subtraction.

Unlike the counter, the adder app does not have to run in real time. It slows down on overflows. Step-by-step mode allows to see every move.

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