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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).
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 ...
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 ...
Download as PDF; Printable version; ... For those make sure the piped link avoiding the redirect is in this template. ... for IEEE 802.15.1. See also
William Kahan, primary architect of the original IEEE 754 floating-point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ...
Download as PDF; Printable version; In other projects ... IEEE 754-2008; IEEE 754-2008 revision; IEEE 754-2019; IEEE 854-1987; IEEE 1003; IEEE 1028; IEEE 1164; IEEE 1275;
In the IEEE 754 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 single precision and, more recently, base-10 representations (decimal floating point).
Because the significand for the IEEE 754 decimal formats is not normalized, most values with less than 16 significant digits have multiple possible representations; 1000000 × 10 −2 =100000 × 10 −1 =10000 × 10 0 =1000 × 10 1 all have the value 10000.