Normal number (computing)

In computing, a normal number is a non-zero number in a floating-point representation 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^{E_{\text{min}}} where b is the base (radix) of the format (like common values 2 or 10, for binary and decimal number systems), and E_{\text{min}} depends on the size and layout of the format. Similarly, the magnitude of the largest normal number in a format is given by b^{E_{\text{max}}}\cdot\left(b - b^{1-p}\right) where p is the precision of the format in digits and E_{\text{min}} is related to E_{\text{max}} as: E_{\text{min}}\, \overset{\Delta}{\equiv}\, 1 - E_{\text{max}} = \left(-E_{\text{max}}\right) + 1 In the IEEE 754 binary and decimal formats, b, p, E_{\text{min}} , and E_{\text{max}} have the following values: For example, in the smallest decimal format in the table (decimal32), the range of positive normal numbers is 10 −95 through 9.999999 × 10 96 . Non-zero numbers smaller in magnitude than the smallest normal number are called subnormal numbers (or denormal numbers). Zero is considered neither normal nor subnormal.

In computing, a normal number is a non-zero number in a floating-point representation 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^{E_{\text{min}}} where b is the base (radix) of the format (like common values 2 or 10, for binary and decimal number systems), and E_{\text{min}} depends on the size and layout of the format. Similarly, the magnitude of the largest normal number in a format is given by b^{E_{\text{max}}}\cdot\left(b - b^{1-p}\right) where p is the precision of the format in digits and E_{\text{min}} is related to E_{\text{max}} as: E_{\text{min}}\, \overset{\Delta}{\equiv}\, 1 - E_{\text{max}} = \left(-E_{\text{max}}\right) + 1 In the IEEE 754 binary and decimal formats, b, p, E_{\text{min}} , and E_{\text{max}} have the following values: For example, in the smallest decimal format in the table (decimal32), the range of positive normal numbers is 10 −95 through 9.999999 × 10 96 . Non-zero numbers smaller in magnitude than the smallest normal number are called subnormal numbers (or denormal numbers). Zero is considered neither normal nor subnormal.

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