Extreme Exponents

The representations of extreme exponents are as follows.

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.

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.