From what I have seen, division is a highly expensive operation in terms of time or area (tradeoff). It is usually implemented as an operation of continuous subtraction of a number from another number to get the quotient bits.
While I understand how addition, subtraction and multiplication are implemented, there is some confusion surrounding division. I have 3 interrelated questions.
Q1: If division is merely recursion of subtractions until we are left with remainder, how would one get a fixed point output i.e output with both integer and fraction parts; since an integer quotient represents how many times we did subtraction in a loop.
Q2: How would one deal with recurring decimal numbers as quotient? I assume through round-off i.e we do not care if result is recurring decimal or not, we just calculate the result to certain digits of fractional part.
Q3: Provided that I have a divider IP that outputs remainder and quotient, how would I get the fractional part of the output since the remainder does not actually equal the fractional part?