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What is Floating Point?

David White
David White

Despite its concrete-sounding name, a floating point is something that technically doesn’t exist. People can’t prove its existence, 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 of a number, an approximation of an actual number. It doesn’t exist on number lines or on the pages of mathematics textbooks, however. Floating points form the basis of computer calculations.

Man holding computer
Man holding computer

Usually, these 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 often complex data interactions that make up a computer’s most basic and more complicated functions. Showing the date and time, for example, could take a few or perhaps a large handful of calculations, depending on a number of variables. Displaying options and results for graphic-intensive software programs, however, might require calculations numbering in the millions.

A sometimes interesting byproduct of these calculations is that numbers that would be equal on a number line or in numerical equations can co-exist. For example, both 0.01 x 10(1) and 1.00 x 10(-1) are equal to 0.1 if we write them as parts of an equation, but floating point calculations allow both simply because they are written differently. Equations, which tend to want to simplify things as much as possible, are not floating point calculations, and vice versa.

One issue surrounding such calculations that is quite unpopular with makers of financial software, the users of which require exact calculations down into the smaller sides of the decimal, is that the numbers are not at all definite. It’s all well and good to tell the time and date using this type of calculation, but determining a multinational company’s net worth for a given fiscal year needs a much more definite numerical accounting than the inherent random result that a floating point calculation will provide. The very words suggest that the numbers are not at all stable, and that kind of insecurity makes financial experts uncomfortable.

Floating point arithmetic is popular with makers of hardware and software the world over nonetheless. One of the most popular standards nowadays is the IEEE standard, an international set of guidelines for structuring and analyzing these computations. This standard forms the basis of many programming languages and security protocols.

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      Man holding computer