computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, e ...

, a normal number is a non-zero number in a

floating-point representation In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can ...

which is within the balanced range supported by a given floating-point format: it is a floating point number that can be represented without leading zeros in its significand. The magnitude of the smallest normal number in a format is given by ''b''^''emin'', where ''b'' is the base (radix) of the format (usually 2 or 10) and ''emin'' depends on the size and layout of the format. Similarly, the magnitude of the largest normal number in a format is given by :''b''^''emax'' × (''b'' − ''b''^1−''p''), where ''p'' is the precision of the format in digits and ''emax'' is (−''emin'')+1. In the

IEEE 754 The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found i ...

binary and decimal formats, ''b'', ''p'', ''emin'', and ''emax'' have the following values: For example, in the smallest decimal format, the range of positive normal numbers is 10⁻⁹⁵ through 9.999999 × 10⁹⁶. Non-zero numbers smaller in magnitude than the smallest normal number are called subnormal (or denormal) numbers. Zero is neither normal nor subnormal.

References

{{DEFAULTSORT:Normal Number (Computing) Computer arithmetic

See also

References