floating-point representation system
Noun: A system for representing real numbers in computing and digital systems where a number is expressed as a significant digit (the mantissa) multiplied by a base raised to an exponent. This allows for the representation of a wide range of values, from very small to very large, by allowing the decimal (or binary) point to "float" based on the exponent value.
This term is used almost exclusively in the context of computer science, mathematics, and engineering to describe the standard method for handling non-integer numbers in digital computations. - The result of the calculation was stored using a floating-point representation system. - Understanding the floating-point representation system is crucial for writing accurate numerical software.
- Floating-point arithmetic: Refers to the mathematical operations (addition, subtraction, etc.) performed on numbers represented in this system.
- Floating-point unit (FPU): The part of a computer's processor specifically designed to carry out operations on floating-point numbers.
- Floating-point error/round-off error: The inaccuracy that can arise because a real number must be approximated within the finite precision of the system.
- Floating-point notation: A synonymous term for the representation system itself.
- Floating-point number (or float): A single number represented within this system (e.g., or ).
- Fixed-point representation: A contrasting system where the decimal point is in a fixed, predetermined position.
- Scientific notation (in a general mathematical sense, though this specifically refers to the computational implementation).
- Mantissa/Significand: The part of the representation that contains the significant digits of the number.
- Exponent: The part of the representation that indicates the power to which the base is raised, determining the position of the decimal point.
- IEEE 754: The ubiquitous international technical standard that defines formats and rules for floating-point arithmetic in most computers.
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a radix numeration system in which the location of the decimal point is indicated by an exponent of the radix; in the floating-point representation system, 0.0012 is represented as 0.12-2 where -2 is the exponent
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