Signed zero

Article summary

Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, and −0, +0 and 0 are three ways of writing the same number. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the sign–magnitude and ones' complement signed number representations for integers, and in most floating-point number representations. The number 0 is typically expressed as +0. The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Its arithmetic can be considered to model a variant of the extended real number line (the real numbers including additional numbers +∞ and −∞). In IEEE 754 arithmetic, = −∞ and = +∞; the divisions and return "Not a Number" (NaN). Negatively signed zero echoes the mathematical analysis concept of approaching 0 from below as a one-sided limit, which may be denoted by x → 0 − , x → 0−, or x → ↑0. The notation "−0" may be used informally to denote a negative number that has been rounded to zero.…

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