### Calculator Forensics

Introduction
The Forensics Algorithm.
Hints and Tricks For Obtaining Guard Digits.
Computing the Forensics Algorithm in Radians.
Forensics Algorithm Background.
Results Table Sorted By Result.
Results Table Sorted By Calculator Model.

Introduction

"Calculator forensics" is a term I've coined which seeks to answer the questions of who originally designed a particular calculator's chip set, what features of a particular calculator have been borrowed from earlier designs, and how has calculator technology spread among the manufacturers.

The superficial answer to the first question is "open the calculator and look at the chip." With some calculators, this is a practical answer. However, many calculators cannot be opened without damaging the case or are constructed in such a manner that it is not practical to view the part number. Or even worse, the identifying markings on the chip's package are not useful (e.g. they are an ambiguous "house number," or the part number prefix or manufacturer's logo are not recognized). For one calculator in my collection, the only marking on the chip's package is "IC" in big letters, which is not particularly helpful!

Answers to the second and third questions require the collection of observations from numerous calculators, coupled with a review of any other published data.

The Calculator Forensics Process

The calculator forensics process includes reviewing any published technical documentation, observing the physical attributes of the calculator (e.g. number of display digits, internal construction, cosmetic features), the keyboard layout, the key assignments, display font, and indirectly the embedded algorithms.

Published technical documentation is particularly difficult to obtain. For the older calculators and their chip sets, data books, service manuals, and secondary source data are difficult to locate. Further, for many of the newer calculators, design information is rarely published. Patents can sometimes provide useful information; Hewlett-Packard and Texas Instruments calculator patents frequently (but not always) describe products that were actually manufactured.

Physical attributes, keyboard layout, display font, and key assignments can be directly observed once you obtain physical possession of the calculator. Despite the limitations discussed above, disassembly may provide further clues about the history of that calculator. For example, disassembly to read date codes off chips or other components is frequently the only way to ascertain the approximate manufacture date of the calculator.

The Forensics Evaluation Algorithm

Observations regarding the embedded algorithms are also useful in identifying related calculators. Making these observations requires observing the results produced by the embedded algorithms. I believe a standardized evaluation procedure helps in observing the results of embedded algorithms and in comparing these observations to other calculators. The evaluation algorithm I have chosen to use (with the calculator in degrees mode) is:

arcsin (arccos (arctan (tan (cos (sin (9) ) ) ) ) )

The keystroke sequence (ignoring 2nd, INV, or ARC keys) is typically: 9, sin, cos, tan, arctan, arccos, arcsin. This algorithm usually produces different results on different calculator models (otherwise it would have no value as an evaluation and comparison tool).

In using this algorithm for forensics purposes, it additionally becomes desirable to obtain any extra hidden guard digits that may be present. Some finagling is usually required to get at the hidden guard digits, and care must be taken to avoid the rounding of intermediate results as happens on some calculators (see hints and tricks). Unfortunately, there is no single best method for obtaining these guard digits.

See the forensics algorithm background discussion for more information on this algorithm and its history.

Results Tables

The results of the evaluation algorithm, for forensics purposes, is of limited use without being able to compare it to the results from other calculators. To this end, two tables have been constructed which provide the results from many calculators in my collection along with those from other collectors.

Results table sorted by result.

Results table sorted by calculator model.

Postscript

Some people may be tempted to base their evaluation of the "quality" of a vintage calculator on the accuracy and precision of that calculator. However, these are only two components by which to evaluate a vintage calculator. Probably the most important factor to consider in evaluating any vintage calculator is this: does it still work twenty-plus years after it was manufactured? Any product that still functions as well today as it did the day it rolled off the production line over two decades ago is a quality vintage calculator, and a testament to the engineers that designed it.

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Last updated August 15, 2002