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Here the 'IEEE 754 double value' resulting of the 15 bit figure is 3.330560653658221E-15, which is rounded by Excel for the 'user interface' to 15 digits 3.33056065365822E-15, and then displayed with 30 decimals digits gets one 'fake zero' added, thus the 'binary' and 'decimal' values in the sample are identical only in display, the values ...
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
IEEE 754 specifies additional floating-point types, such as 64-bit base-2 double precision and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and properties of ...
Decimal64 supports 'normal' values that can have 16 digit precision from ±1.000 000 000 000 000 × 10 ^ −383 to ±9.999 999 999 999 999 × 10 ^ 384, plus 'denormal' values with ramp-down relative precision down to ±1.×10 −398, signed zeros, signed infinities and NaN (Not a Number).
Template documentation Note that not all articles use the standards number as their title. For those make sure the piped link avoiding the redirect is in this template.
On Java before version 1.2, every implementation had to be IEEE 754 compliant. Version 1.2 allowed implementations to bring extra precision in intermediate computations for platforms like x87. Thus a modifier strictfp was introduced to enforce strict IEEE 754 computations. Strict floating point has been restored in Java 17.
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