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A number is normalized if the exponent field contains other than all 1's or all 0's.
The exponent field contains a biased exponent, where the bias is 127 in single-precision, 1023 in double-precision, and 16,383 in extended-precision. Thus, the exponent of a normalized floating point number is in the range -126 to 127 inclusive for single-precision, and in the range -1022 to 1023 inclusive for double-precision. For extended-precision the range is -16,382 to 16,383.
There is an implicit bit associated with both single- and
double-precision formats. The implicit bit is not
explicitly stored anywhere (thus its name). Logically, for
normalized operands the implicit bit has a value of 1 and
resides immediately to the left of the binary point (in the
position). Thus the implicit bit and fraction field
together can represent values in the range 1 to
inclusive for single-precision, and in the range 1 to
inclusive for double-precision. For extended-precision,
there is no such bit, therefore the field can represent
values in the range 1 to
Thus normalized single-precision numbers can be in the range (plus
or minus)
to
inclusive.
Normalized double-precision numbers can be in the range (plus
or minus)
to
inclusive.
Normalized extended-precision numbers can be in the range (plus
or minus)
to
inclusive.