Floating Point

One of the most basic requirements of a computer is how is it to store and calculate numbers with decimal points i.e. Real Numbers. For example

1.44566 + 2.33 x (-3.21)

After all, all data in a computer are stored and handled as binary numbers such as
10111100 11001010 11100000

So an engineering committee was set up many years ago with the purpose of coming up with a standard way of representing a decimal number as a binary number (there are many ways of doing it).

If computer makers then followed this standard, a computer program running on one computer would also work in the same way on another machine that also followed the standard. A bit like all CD players will work with a standard sized CD disk, it would be chaos if everyone made different sized disks.

For decimal numbers this standard is the IEEE-754 'Floating Point' standard. It works by breaking up the number into three parts.
1. A single binary bit shows if the number is positive or negative
2. A part that represents the rough size of the number (exponent)
3. A part that shows the precise detail of the number (the 'fraction')

Most CPU's have a 'floating point' unit as part of the chip. This carries out all floating point calculations, for example the XBox or PS3 will be making heavy use of their FPU's as they display the graphics in the latest game.

2020-10