Floating Point

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Floating Point

Floating point is a computer number format that represents real numbers using a sign, an exponent, and a mantissa, allowing for a wide range of values to be represented with varying degrees of precision.

What does Floating Point mean?

Floating point is a number representation scheme that uses a floating radix point to represent numbers. The radix point, which is typically represented as a decimal point, separates the number’s significant digits from its exponent. The exponent is an integer that indicates the power to which the radix is raised to obtain the value of the number.

Floating point numbers are often used to represent very large or very small numbers, which would be difficult or impossible to represent using a fixed-point notation. For example, the floating point number 1.2345e+10 represents the number 12,345,000,000.

Floating point numbers are stored in a computer’s Memory using a variety of formats, including the IEEE 754 Standard. The IEEE 754 standard defines a variety of floating point formats, including single-precision, double-precision, and extended-precision formats.

Applications

Floating point numbers are used in a wide variety of applications, including:

  • Scientific Computing: Floating point numbers are used to represent the results of scientific calculations, which often involve very large or very small numbers.
  • Financial calculations: Floating point numbers are used to represent monetary values, which can Range from very small amounts to very large amounts.
  • Computer graphics: Floating point numbers are used to represent the coordinates of objects in 3D space, which can range from very small values to very large values.
  • Audio processing: Floating point numbers are used to represent the amplitude of sound waves, which can range from very small values to very large values.

History

The concept of floating point was first proposed in the 19th century by Charles Babbage. However, it was not until the 1950s that floating point arithmetic was implemented in electronic computers.

The first floating point format to be widely adopted was the IBM 704 floating point format. This format was used in a variety of computers, including the IBM 7090 and the IBM 7094.

In 1985, the IEEE 754 standard for floating point arithmetic was published. This standard defined a variety of floating point formats, including single-precision, double-precision, and extended-precision formats. The IEEE 754 standard has been widely adopted by computer manufacturers, and it is now the most common floating point format in use today.