# \$MinMachineNumber

is the smallest positive machineprecision number that can be represented in normalized form on your computer system.

# Details # Examples

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## Basic Examples(1)

The smallest hardware floating-point number that can be put in normalized form:

## Scope(3)

Machine numbers smaller than \$MinMachineNumber are represented as subnormal machine numbers: This is still a machine number:

However, x has not gained accuracy relative to \$MinMachineNumber:

Find the smallest positive normalized machine number algorithmically: Find the smallest positive subnormal machine number algorithmically: ## Properties & Relations(4)

Compute the minimum exponent in binary for machine arithmetic:

\$MinMachineNumber has that smallest exponent and all bits but the first set to 0 in the significand:

Subnormal machine numbers have the minimum exponent and a leading 0 bit in the significand: \$MinMachineNumber/252 produces that smallest positive subnormal number: Further division produces a machine zero:

\$MaxMachineNumber×\$MinMachineNumber is 4.×(1.-\$MachineEpsilon/2):

Accuracy[\$MinMachineNumber] equals Accuracy[0.]:

## Possible Issues(2)

Computations with machine numbers smaller than \$MinMachineNumber can lose all significant digits: Use SetPrecision to convert a machine number to arbitrary precision and avoid underflow:

The reciprocal of \$MaxMachineNumber is smaller than \$MinMachineNumber: Introduced in 1991
(2.0)
|
Updated in 2003
(5.0)
2018
(11.3)