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I read that the Chinese abacus is well suited to hex numbers as well as decimal, because its columns have 5 beads in the lower part, and 2 in the upper.

Is there any efficient algorithm for translating the two with the Chinese abacus?

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I think the issue is not so much that you can translate decimal to hex numbers with the Abacus (in fact, it's not clear to me how to do this), but that you can use the Abacus to do calculations in hex. If a bead in the upper part represents 5 and a bead in the low part represents 1, then you can represent numbers from 0 to 15 in one column, that is, one hex digit.

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