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A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point arithmetic is often used to allow very small and very large real numbers that require fast processing times.
By contrast, in computer science, addition and multiplication of floating point numbers are not associative, as different rounding errors may be introduced when dissimilar-sized values are joined in a different order. [7] To illustrate this, consider a floating point representation with a 4-bit significand:
The 68881 has eight 80-bit data registers (a 64-bit mantissa plus a sign bit, and a 15-bit signed exponent). [2] It allows seven different modes of numeric representation, including single-precision floating point, double-precision floating point, extended-precision floating point, integers as 8-, 16- and 32-bit quantities and a floating-point Binary-coded decimal format.
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
A floating-point unit (FPU), numeric processing unit (NPU), [1] colloquially math coprocessor, is a part of a computer system specially designed to carry out operations on floating-point numbers. [2] Typical operations are addition , subtraction , multiplication , division , and square root .
Cool Math Games (branded as Coolmath Games) [a] is an online web portal that hosts HTML and Flash web browser games targeted at children and young adults. Cool Math Games is operated by Coolmath LLC and first went online in 1997 with the slogan: "Where logic & thinking meets fun & games.".
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