16 1 = 1.6 = 1 + 2/16 + 3/162 + r … 16 2 = 9.6 = 2 + 3/16 + 4/162 + r … Hence, a number with digits in one base may not have terminal m representation in another base. (e.g., It is not just irrationals that are a problem consider ). Consider = .115 if b = 10 and = 2, then r m = .11 chopping r = .12 symmetric rounding (r+.5bc-m-1 and then chop) r Most computers chop instead of round off. IEEE compliant CPUs can do both and there may be a system call to switch, which is usually not user accessible. Note: When the rounding changes, almost all nontrivial codes break.
16 r 1 = 1.6 = 1 + 2/16 + 3/162 + … 16 r 2 = 9.6 = 2 + 3/16 + 4/162 + … Hence, a number with m digits in one base may not have terminal representation in another base. It is not just irrationals that are a problem (e.g., consider ). Consider r = .115 if b = 10 and m = 2, then r = .11 chopping r = .12 symmetric rounding (r+.5bc-m-1 and then chop) Most computers chop instead of round off. IEEE compliant CPUs can do both and there may be a system call to switch, which is usually not user accessible. Note: When the rounding changes, almost all nontrivial codes break.
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