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A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
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 from 10 3 = 1000 and 2 10 - 1 = 1023.)
Thus only 23 fraction bits of the significand appear in the memory format, but the total precision is 24 bits (equivalent to log 10 (2 24) ≈ 7.225 decimal digits) for normal values; subnormals have gracefully degrading precision down to 1 bit for the smallest non-zero value.
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 the unused range from 10 3 = 1000 to 2 10 - 1 = 1023.)
The decimal digits of ... Integers: 3; Fractions: Approximate fractions include ... The first 36 digits in ternary (base 3) ...
- Different understanding of significand as integer or fraction, and acc. different bias to apply for the exponent (for decimal64 what is stored in bits can be decoded as base to the power of 'stored value for the exponent minus bias of 383' times significand understood as d 0. d −1 d −2 d −3 d −4 d −5 d −6 d −7 d −8 d −9 d ...
This gives from 33 to 36 significant decimal digits precision. If a decimal string with at most 33 significant digits is converted to the IEEE 754 quadruple-precision format, giving a normal number, and then converted back to a decimal string with the same number of digits, the final result should match the original string.
Having an odd prime number of digits is not enough to guarantee that a repunit is prime; for instance, 21 = 111 4 = 3 × 7 and 111 = 111 10 = 3 × 37 are not prime. In any given base b, every repunit prime in that base with the exception of 11 b (if it is prime) is a Brazilian prime. The smallest Brazilian primes are