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For example, the decimal number 123456789 cannot be exactly represented if only eight decimal digits of precision are available (it would be rounded to one of the two straddling representable values, 12345678 × 10 1 or 12345679 × 10 1), the same applies to non-terminating digits (. 5 to be rounded to either .55555555 or .55555556).
A 2-bit float with 1-bit exponent and 1-bit mantissa would only have 0, 1, Inf, NaN values. If the mantissa is allowed to be 0-bit, a 1-bit float format would have a 1-bit exponent, and the only two values would be 0 and Inf. The exponent must be at least 1 bit or else it no longer makes sense as a float (it would just be a signed number).
In base ten, a sixteen-bit integer is certainly adequate as it allows up to 32767. However, this example cheats, in that the value of n is not itself limited to a single digit. This has the consequence that the method will fail for n > 3200 or so. In a more general implementation, n would also use a multi-digit
The element pc requires ten blocks of memory of the size of pointer to char (usually 40 or 80 bytes on common platforms), but element pa is only one pointer (size 4 or 8 bytes), and the data it refers to is an array of ten bytes (sizeof * pa == 10).
Other languages provide only one-based array types, where each index starts at 1; this is the traditional convention in mathematics for matrices and mathematical sequences. A few languages, such as Pascal and Lua, support n-based array types, whose minimum legal indices are chosen by the programmer. The relative merits of each choice have been ...
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.
The leading digit is between 0 and 9 (3 or 4 binary bits), and the rest of the significand uses the densely packed decimal (DPD) encoding. The leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand are combined into the five bits that follow the sign bit. This is followed by a fixed-offset exponent continuation field.
E.g. binary128 has approximately the same precision as a 34 digit decimal number. log 10 MAXVAL is a measure of the range of the encoding. Its integer part is the largest exponent shown on the output of a value in scientific notation with one leading digit in the significand before the decimal point (e.g. 1.698·10 38 is near the largest value ...