UPDATED 2014-03-25: There is another Mathcad FIF function input style available (three scalar values), so I included a couple examples. It should be more versatile than the text string approach.
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UPDATED 2014-03-24: OOPS! I forgot the .pdf file I promised. It is now included in the .zip file.
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The purpose of this worksheet is to demonstrate various Mathcad techniques for dealing with length dimensions in feet-inches-fractions (FIF) format. Because the USA's ponderous conversion to the SI system is limited mostly to the federal government, most architectural, structural engineering, and plant piping dimensions in the United States are still provided in the "quaint" US Customary Units (USCU) system, with the added burden of using FIF values instead of decimal feet like we do for surveying and most non-structural/non-piping civil engineering.
Because of Mathcad's brilliant handling of units, it deals with FIF values as well or better than any other tool I know of, including FIF-capable calculators (which, sadly, are not RPN). Unfortunately, Mathcad does not have an elegant way to display results in FIF format. However, this can be done after a fashion, as this worksheet shows. Mathcad also cannot display numbers in degrees-minutes-seconds (DMS) and hours-minutes-seconds (HMS) formats, but that is a topic for another day.
Four data input methods are shown: (a) using Mathcad's FIF function on dimensions provided as strings, (b) using the simple addition of feet, inches, and fractions, (c) using a four-element vector, and (d) using a table with multiple FIF dimensions. Two versions of a program are included to break down decimal lengths into feet, inches, and reduced fractions and then display the FIF components. Various examples are provided.
This worksheet is based ultimately on an FIF program I wrote in 1984 for the HP-41CX calculator (see http://www.hpmuseum.org/software/41/41feet.htm). The HP-41CX program performs FIF artithmetic using a two-register RPN stack, can use ANY counting number as the basis for fractions of an inch, and can even use trig functions, which is useful for FIF triangle solutions. I later upgraded this program by simplifying the algorithm, but there is one minor bug I should be chasing so I haven't published it yet. There is also an HP-42S version of the upgraded program that is also unpublished due to the same bug. Fixing these programs is on my never-ending to-do list.
In 2004, I created an Excel spreadsheet for adding and subtracting multiple FIF values and for calculating areas and volumes. I have included a copy of this spreadsheet (in template form) for your use. An architect friend, whom I supplied this to years ago, told me recently that he still uses it.
The calculator programs are the most clever (the fraction reduction subroutine is based on the FR program in the famous PPC ROM) and produce the best formatted output, but they are very slow compared to the virtually instantaneous results provided by the Excel spreadsheet and this Mathcad worksheet. Because Mathcad natively handles units (unlike Excel) , this worksheet contains the simplest algorithms of the three. However, Mathcad has the weakest formatting tools for FIF, so this is one of the few occasions where I think the Excel spreadsheet is more usable than I will ever be able to make this Mathcad worksheet. On the other hand, if you need FIF capabilities in a Mathcad worksheet, then there is no substitute for having it, which this worksheet provides.
NOTE: The attached .zip file contains a Mathcad Prime 3.0 worksheet (.mcdx) and—for those of you who are still using earlier verisions of Mathcad—an Adobe Acrobat printout (.pdf) of the worksheet so can see how it is put together.
One can never get tired of this subject.
Thanks for the excellent history discussion in your post.
For the record, what is RPN?
RPN stands for Reverse Polish Notation, which is the operating system used on most Hewlett-Packard calculators. My HP collection includes the following models: HP-35, HP-55, HP-34C, HP-41C, HP-41CX, HP-42S (my daily driver), HP-48G+, HP-32SII, HP10B (which I won in a contest and is the only algebraic logic HP calc I own), and HP35S.
http://www.hpmuseum.com/ is the best site on the internet for historical information about HP calculators.