Once we know how to represent very large, very small and fractional numbers, we need to know how to manipulate them. Obviously, the standard operations, addition, subtraction, multiplication and division, must be accommodated. Some chips also include reciprocal (1/x) and square root instructions.

A CPU that can perform floating point operations must have special hardware circuits, since the standard adder cannot do the job, at least not without some help. Also, new kinds of errors crop up. We will consider only addition and multiplication herein since subtraction and division are very similar.