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Mesh data is usually stored using 32-bit single-precision floats for the vertices, however in some situations it is acceptable to reduce the precision to only 16-bit half-precision, requiring only half the storage at the expense of some precision. Mesh quantization can also be done with 8-bit or 16-bit fixed precision depending on the requirements.
Each of these number systems is a positional system, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hexadecimal weights are powers of 16. To convert from hexadecimal or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. For example:
The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. 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 ...
The "decimal" data type of the C# and Python programming languages, and the decimal formats of the IEEE 754-2008 standard, are designed to avoid the problems of binary floating-point representations when applied to human-entered exact decimal values, and make the arithmetic always behave as expected when numbers are printed in decimal.
7 decimal digits for decimal32, 16 decimal digits for decimal64, 34 decimal digits for decimal128. Algorithms, with code, for correctly rounded conversion from binary to decimal and decimal to binary are discussed by Gay, [59] and for testing – by Paxson and Kahan. [60]
This gives from 6 to 9 significant decimal digits precision. If a decimal string with at most 6 significant digits is converted to the IEEE 754 single-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. If an IEEE 754 single ...
Conversion of the simple sum of two digits can be done by adding 6 (that is, 16 − 10) when the five-bit result of adding a pair of digits has a value greater than 9. The reason for adding 6 is that there are 16 possible 4-bit BCD values (since 2 4 = 16), but only 10 values are valid (0000 through 1001).
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.