What is Floating Point?
Despite its concrete-sounding name, a floating point is something that technically doesn’t exist. You can’t prove the existence of a floating point, yet it is used millions of times a day in computer operations. How and why this happens is fascinating to many people. A floating point is, at its heart, a number. In technical terms, it is a digital representation for a number, an approximation of an actual number. Floating points don’t exist on number lines or on the pages of mathematics textbooks, however. Floating points form the basis of computer calculations. Usually, floating point numbers are a combination of integers and their various multipliers. In computer terms, the number two is usually the base in such an operation. Using such a base and various exponents, the computer will perform operations by the millions. The vast majority of these operations are powered by floating point numbers. The idea behind floating point numbers is to generate enough random numbers to power the of
Computers always need some way of representing data, and ultimately those representations will always boil down to binary (0s and 1s). Integers are easy to represent (with appropriate conventions for negative numbers, and with well-specified ranges to know how big the representation is to start with) but non-integers are a bit more tricky. Whatever you come up with, there’ll be a problem with it. For instance, take out own normal way of writing numbers in decimal: that can’t (in itself) express a third. You end up with a recurring 3. Whatever base you come up with, you’ll have the same problem with some numbers – and in particular, “irrational” numbers (numbers which can’t be represented as fractions) like the mathematical constants pi and e are always going to give trouble. You could store all the rational numbers exactly as two integers, with the number being the first number divided by the second – but the integers can grow quite large quite quickly even for “simple” operations, and
