

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 singleprecision, 1023 in doubleprecision, and 16,383 in extendedprecision. Thus, the exponent of a normalized floating point number is in the range 126 to 127 inclusive for singleprecision, and in the range 1022 to 1023 inclusive for doubleprecision. For extendedprecision the range is 16,382 to 16,383.
There is an implicit bit associated with both single and doubleprecision 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 singleprecision, and in the range 1 to inclusive for doubleprecision. For extendedprecision, there is no such bit, therefore the field can represent values in the range 1 to
Thus normalized singleprecision numbers can be in the range (plus or minus) to inclusive.
Normalized doubleprecision numbers can be in the range (plus or minus) to inclusive.
Normalized extendedprecision numbers can be in the range (plus or minus) to inclusive.