#
Extreme Exponents

The representations of extreme exponents are as follows.

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Zero (signed)

Zero (signed) is represented by an exponent of zero and a fraction of zero.

##
Subnormal Number

The form of a subnormal number is:

(-1) ^{sign} * 2 ^{1-bias} *0.f

where **f** is the bits in the significand.

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Signed Infinity

Signed infinity--that is, affine infinity--is represented by the largest value that the exponent can assume (all ones), and a zero fraction.

##
Not a Number (NaN)

Not a Number (NaN) is represented by the largest value that the exponent can assume (all ones), and a nonzero fraction.

Normalized `REAL` and `DOUBLE` `PRECISION` numbers have an implicit leading bit that provides one more bit of precision than is stored in memory. For example, IEEE double precision provides 53 bits of precision: 52 bits stored in the fraction, plus the implicit leading 1.