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The 8 decimal values whose digits are all 8s or 9s have four codings each. The bits marked x in the table above are ignored on input, but will always be 0 in computed results. (The 8 × 3 = 24 non-standard encodings fill in the gap between 10 3 = 1000 and 2 10 = 1024.
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]
That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hexadecimal "10" is the same as a decimal "16" and a hexadecimal "20" is the same as a decimal "32".
This is a binary format that occupies at least 79 bits (80 if the hidden/implicit bit rule is not used) and its significand has a precision of at least 64 bits (about 19 decimal digits). The C99 and C11 standards of the C language family, in their annex F ("IEC 60559 floating-point arithmetic"), recommend such an extended format to be provided ...
Conversion of the fractional part: Consider 0.375, the fractional part of 12.375. To convert it into a binary fraction, multiply the fraction by 2, take the integer part and repeat with the new fraction by 2 until a fraction of zero is found or until the precision limit is reached which is 23 fraction digits for IEEE 754 binary32 format.
Although log 10 ( 2 64) ≈ 19.266, this format is usually described as giving approximately eighteen significant digits of precision (the floor of log 10 ( 2 63), the minimum guaranteed precision). The use of decimal when talking about binary is unfortunate because most decimal fractions are recurring sequences in binary just as 2 / 3 is
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[64] 62: Can be notated with the digits 0–9 and the cased letters A–Z and a–z of the English alphabet. 64: Tetrasexagesimal: I Ching in China. This system is conveniently coded into ASCII by using the 26 letters of the Latin alphabet in both upper and lower case (52 total) plus 10 numerals (62 total) and then adding two special characters ...