floating-point notation
A computer scientist writes a number in floating-point notation on a whiteboard.
Noun: A system for representing real numbers in computing and mathematics where a number is expressed as a significand (or 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.
Floating-point notation is the standard method for approximating real numbers in digital computers. It is used to handle numbers with fractional parts and numbers that are too large or too small for fixed-point notation. - The result of the scientific calculation was stored in floating-point notation to preserve its precision. - Understanding floating-point notation is essential for programmers working on numerical analysis or graphics.
- Floating-point arithmetic: Calculations performed using numbers in floating-point notation. This arithmetic can sometimes lead to rounding errors due to the finite precision of computer representations.
- The discrepancy in the final sum was due to an error in floating-point arithmetic.
- Floating-point unit (FPU): A part of a computer processor specially designed to carry out operations on floating-point numbers efficiently.
- Floating-point representation (n): Another term for the system of floating-point notation.
- Floating-point number (n): A specific number expressed in this notation (e.g., or ).
- Fixed-point notation (n): A contrasting system where the decimal point is in a fixed, predetermined position.
- Scientific notation (in a general mathematical context, though scientific notation typically uses base 10, while floating-point in computers uses base 2).
- Significand/Mantissa: The part of a floating-point number that contains its significant digits.
- Exponent: The part that determines the position of the radix point (decimal or binary point).
- Precision: The number of significant digits the significand can hold, which affects the accuracy of the representation.
- Underflow/Overflow: Conditions that occur when a number is too close to zero or too large, respectively, to be represented in the given floating-point format.
A computer scientist writes a number in floating-point notation on a whiteboard.
- 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