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Document ID: EMON-3M3REM

IBM WorkPad - Notes on Binary-Based Calculators

Applicable to: United States

There have been complaints about calculator round-off "errors" associated with the display of "0.0". These type of errors are symptomatic of binary-based calculators that only approximate decimal equivalents, and are shared by many other computer calculators.

For example: subtract "0.1" eighteen times from "1.8" until you expect to see "0.0" as the result. The Pilot Calculator will display "-4.1633363e-16". The desktop calculator on a Macintosh is more accurate, but it still does not display "0.0", rather a very small number in scientific notation: "-2.30393E-19". This value is in fact 2.30393/10000000000000000000. This is a very small number which represents the cumulative error of eighteen binary approximations of "0.1" added together (or in this case, all subtracted from 1.8).

Note that approximations of "0.0" in scientific notation will appear on your WorkPad calculator only after numerous repetitive mathematical operations. For example, if you subtract "0.1" seventeen times or fewer to arrive at zero, "0.0" will be displayed by version 2.0 of SlimCalc. We are confident that the calculator should yield satisfactory results for the vast majority of the calculations required by WorkPad users.

The reason that "0.0" does not always result on the SlimCalc or Mac Desktop calculators (e.g. if "0.1" is subtracted eighteen times or more), is because of an inherent trade-off with the calculators' computational accuracy for complex mathematical operations (e.g. log functions). We have strived to maintain a sound balance between rounding results to convenient decimal equivalents and preserving complex computational accuracy.

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