Definition
Floating-Point Arithmetic
Floating-point arithmetic is a method used in computing and numerical analysis to represent and manipulate real number on digital computers. It allows for the approximation of a wide range of real numbers within a fixed amount of memory by encoding them in a format consisting of a significand (or mantissa), an exponent, and a sign bit. The significand represents the significant digits of the number, the exponent scales the significand by a power of the base (commonly 2, but sometimes 10 or another base), and the sign bit indicates whether the number is positive or negative.
In floating-point arithmetic, a number is typically represented in the form:
This representation enables the efficient calculation with very large and very small numbers, but it comes with limitations in precision and range. Operations using floating-point numbers can introduce rounding errors and precision loss, especially when dealing with very large or very small numbers, or when performing a sequence of calculations. The standards for floating-point arithmetic, such as IEEE 754, define the format for representing floating-point numbers and the rules for arithmetic operations, handling exceptions, and specifying rounding behaviors.