The IEEE double-precision variables are defined as 64-bit entities with the following format: ______________________________________________ | | | SEEEEEEE EEEEEIMM MMMMMMMM MMMMMMMM | | 63 55 47 39 | |______________________________________________| ______________________________________________ | | | MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM | | 31 23 15 7 | |______________________________________________| Hidden Bit In The Mantissa. --------------------------- There is a "hidden" bit in the mantissa part of the IEEE numbers. Since all numbers are normalized, the integer (high) bit of the mantissa is dropped off. The IEEE double-precision range is 2.2E-308 (4.9E-324 de-normalized) to 1.8E+307. The exponent is the power of two needed to correctly position the mantissa to reflect the number's true arithmetic value. If both the exponent and the mantissa have zero in every position, the value is zero. If only the exponent has zero in every position, the value is an unnormal (extremely small). If all bits of the exponent are set to 1 the value is either a positive or negative infinity or a Not a Number (NaN). NaN is sometimes used to indicate an uninitialized variable.