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A decimal data type could be implemented as either a floating-point number or as a fixed-point number. In the fixed-point case, the denominator would be set to a fixed power of ten. In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied.
The otherwise binary Wang VS machine supported a 64-bit decimal floating-point format in 1977. [2] The Motorola 68881 supported a format with 17 digits of mantissa and 3 of exponent in 1984, with the floating-point support library for the Motorola 68040 processor providing a compatible 96-bit decimal floating-point storage format in 1990. [2]
FLOAT (64-bit) DECIMAL, NUMERIC (38 digits) CHAR, VARCHAR, CLOB: BYTE, VARBYTE, BLOB: DATE, TIME, TIMESTAMP (w/wo TIME ZONE) PERIOD, INTERVAL, GEOMETRY, XML, JSON, UDT (User Defined Type) UniData: Dynamic N/A N/A N/A N/A N/A N/A N/A N/A UniVerse: Dynamic N/A N/A N/A N/A N/A N/A N/A N/A Type system Integer Floating point Decimal String Binary ...
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
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.
All integers with seven or fewer decimal digits, and any 2 n for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. In the IEEE 754 standard , the 32-bit base-2 format is officially referred to as binary32 ; it was called single in IEEE 754-1985 .
A fixed-point data type uses the same, implied, denominator for all numbers. The denominator is usually a power of two.For example, in a hypothetical fixed-point system that uses the denominator 65,536 (2 16), the hexadecimal number 0x12345678 (0x1234.5678 with sixteen fractional bits to the right of the assumed radix point) means 0x12345678/65536 or 305419896/65536, 4660 + the fractional ...
decimal64 fits well to replace binary64 format in applications where 'small deviations' are unwanted and speed isn't extremely crucial. In contrast to the binaryxxx data formats the decimalxxx formats provide exact representation of decimal fractions, exact calculations with them and enable human common 'ties away from zero' rounding (in some range, to some precision, to some degree).