Question

Discuss the advantages of using floating-point number systems over fixed-point number systems.

This is for a numerical analysis course.

Answer 1

Floating point numbers are good for, well, floating points, i.e. when you need to express numbers across varying scales. You sacrifice precision to gain range of scale.

On the other hand, fixed point numbers are only suitable at a fixed scale (and they'll over- or underrun if you scale them too much), but you gain precision as long as you remain within the desired scale.

In short: If you multiply a lot but don't add numbers of different scales, use floating points. If you add a lot but don't multiply, use fixed points.

(A good example of a fixed-point use case is anything relating with currency: Essentially, you can fix your unit to be cents, or one hundredth of a cent, and make all your monetary values be integers in that unit.)