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Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
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]
(The 8 × 3 = 24 non-standard encodings fill in the gap from 10 3 = 1000 and 2 10 - 1 = 1023. Benefit of this encoding is access to individual digits by de- / encoding only 10 bits, disadvantage is that some simple functions like sort and compare, very frequently used in coding, do not work on the bit pattern but require decoding to decimal ...
But the decimal number 10 is encoded in hexadecimal as 0A 16 and in BCD as 10 16. Thus a BCD 10 16 interpreted as a hexadecimal encoding erroneously represents the decimal number 16. For example, the SMS protocol uses BCD encoding for dates, so some mobile phone software incorrectly reported dates of messages as 2016 instead of 2010.
Decimal digits is the precision of the format expressed in terms of an equivalent number of decimal digits. It is computed as digits × log 10 base . E.g. binary128 has approximately the same precision as a 34 digit decimal number.
The 53-bit significand precision gives from 15 to 17 significant decimal digits precision (2 −53 ≈ 1.11 × 10 −16). If a decimal string with at most 15 significant digits is converted to the IEEE 754 double-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final ...
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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.