 A division by a number of the form formula_4 or formula_5 often can be converted to such a short sequence.These types of sequences have to always be used for computers that do not have a "multiply" instruction, and can also be used by extension to floating point numbers if one replaces the shifts with computation of "2*x" as "x+x", as these are logically equivalent.Two quantities can be multiplied using quarter squares by employing the following identity involving the floor function that some sources attribute to Babylonian mathematics (2000–1600 BC).