With positional notation, is there any practical usage for negative bases? I recently learned that numbers can be represented in positional notation using a negative base, but I don't see any real practical application of this. So, is there any?
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According to the history section of that wikipedia link yes: Negabinary was implemented in the early Polish computer BINEG, built 1957-59, based on ideas by Z. Pawlak and A. Lazarkiewicz from the Mathematical Institute in Warsaw. Implementations since then have been rare.