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Arithmetic functions (e.g. sqrt, division) are operating on numbers, not bits. These numbers have a digital representation. The first point, when thinking about lookup tables, is to specify numeric ranges and resolutions, then about a suitable numeric format, mostly fixed point.
There's a large amount of contributions related to lookup tables, see the similar threads tab as a first hint. Instead of making edaboard members retelling the stuff that have been already written, you should consult these previous threads. And come back with a more specific question, if necessary.
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