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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".
The 2008 revision of the IEEE 754 floating-point standard adds three decimal types with two binary encodings, with 7-, 16-, and 34-digit decimal significands. [ 13 ] One of the few RISC instruction sets to directly support decimal is IBM's Power ISA , which added support for IEEE 754-2008 decimal floating-point starting with Power ISA 2.05.
Thus, only 10 bits of the significand appear in the memory format but the total precision is 11 bits. In IEEE 754 parlance, there are 10 bits of significand, but there are 11 bits of significand precision (log 10 (2 11) ≈ 3.311 decimal digits, or 4 digits ± slightly less than 5 units in the last place).
Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4. Arbitrary precision floating point numbers are included in the standard library math/bigfloat module. Raku: Rakudo supports Int and FatRat data types that promote to arbitrary-precision integers and rationals.
The resulting significand could be a positive binary integer of 24 bits up to 1001 1111111111 1111111111 b = 10485759 d, but values above 10 7 − 1 = 9 999 999 = 98967F 16 = 1001 1000100101 1001111111 2 are 'illegal' and have to be treated as zeroes. To obtain the individual decimal digits the significand has to be divided by 10 repeatedly.
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For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with 8 decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on.
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