Hexadecimal Research Articles

FORTRAN extended-precision library

Each subroutine in the FORTRAN extended-precision library has been subjected to a set of rigorous performance tests involving thousands of random sample arguments. Master reference programs that compute these functions in 38 hexadecimal digits of precision were used to measure the accuracy of the tested programs. Despite the elaborate care exercised in preparation of the programs in this library, these programs cannot create accuracy where there is none. The accuracy of the computed function value depends on the quality of the input argument as well as the quality of the algorithm used. Seemingly minor contamination of the input value can cause substantial relative errors. The most one can expect and all we have attempted is to minimize any error due to computational method by careful coding, which includes occasional use of guard digits. The average cost of this use of extra precision arithmetic is estimated to be about 10 percent in execution time and somewhat more in storage requirements. We believe this to be a reasonable price to pay for the extra precision of the results.

Another method of converting from hexadecimal to decimal

There is a simple paper-and-pencil method of converting arithmetic a hexadecimal number N to decimal.

The Occurrence of Digits

Let a, x, and b be integers such that x > 1, b > 1, and 0 ? a O, each of the b digits occurs equally often. Hence