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Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial ...
In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the corresponding real number arithmetic operations by rounding any result that is not a floating-point number itself to a nearby floating-point number.
In computing, decimal64 is a decimal floating-point computer number format that occupies 8 bytes (64 bits) in computer memory. Decimal64 is a decimal floating-point format, formally introduced in the 2008 revision [1] of the IEEE 754 standard, also known as ISO/IEC/IEEE 60559:2011. [2]
In computing, decimal128 is a decimal floating-point number format that occupies 128 bits in memory. Formally introduced in IEEE 754-2008, [1] it is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. [2]
A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 2 31 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2 −23) × 2 127 ≈ 3.4028235 ...
The full decimal significand is then obtained by concatenating the leading and trailing decimal digits. The 10-bit DPD to 3-digit BCD transcoding for the declets is given by the following table. b 9 … b 0 are the bits of the DPD, and d 2 … d 0 are the three BCD digits.
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
Floating-point numbers in IEEE 754 format consist of three fields: a sign bit, a biased exponent, and a fraction. The following example illustrates the meaning of each. The decimal number 0.15625 10 represented in binary is 0.00101 2 (that is, 1/8 + 1/32). (Subscripts indicate the number base.)