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Here is a working abacus made out of LEGO parts. This one is a Japanese "soroban", which, for each digit, has 1 "heavenly" bead (worth 5) and 4 "earthly" beads (worth 1 each). You can use it to do arithmetic on numbers up to 13 digits. The slope bricks help you to reset the abacus by sweeping your finger from left to right, like on a regular beaded abacus. I took this design and expanded it quite a bit to make it more sturdy.
I was hoping to make this using LEGO Digital Designer, but the necessary parts are not available in that program. So far I haven't thought of a good way to make one using their EXTREMELY limited parts list.
(These were generated with LeoCAD)