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The Calculator: An Important Engineering Tool

Editor’s note: Also see Ken Coffman’s blog: The HP15C returns as an iPhone app.

With the emergence of hand-sized computers, calculators have lost some of their former prominence, yet they continue to be a convenient and important engineering tool. Electronic calculators have been around since the early TI high-volume calculator ICs which were selling in the 1970s for a few US dollars and at a hundredth the price of 8-bit microprocessors such as the Intel 8080 or the Motorola 6800. Then Motorola designers Chuck Peddle and Will Mathys relocated from the arid zone of Arizona to MOS Technology, in colder, wetter Valley Forge, Pennsylvania, and developed the $20 (in unit quantity, at introduction) 6502. Later, this site produced Atari computers with 6502 microprocessors.

As we marveled at the low introductory, single-unit price of the 6502 in the mid-70s, an IC production engineer at Tektronix pointed out that the chip size of microprocessors and calculators were comparable, and that in volume, they should have comparable prices. They do now, and for quite some time, calculators – especially scientific (in distinction from grocery-store ) calculators – have been implemented as special-purpose or application-specific computers. Scientific calculators now sell for a few dollars – not only the IC but the entire unit, including display and keyboard, battery holder, and in some cases, solar cell. TI continues to be a major supplier of low-cost scientific calculators, though various Asian brands such as Casio have also established a place in the market.

The Venerable HP 45

In the 1970s – the calculator decade – HP also made their mark with the introduction of the HP 35, and shortly thereafter, the HP 45, the first scientific calculator of great impact, predating TI scientific calculators. An HP 45 is shown below, over 40 years later, in front and rear views, with some accessories.

The manual (not shown) was also included in the purchase of the $400 US calculator. The carrying case had a loop on the back for carrying the HP 45 on a pants belt. (The nerd look was more in fashion then.) The security cradle was optional but practical; these were not $15 commodity-grade calculators!

One of the major differences between the HP and TI calculators was the number entry format. TI used the familiar infix notation of mathematics and HP used postfix or RPN (reverse Polish notation, named after the Pole whose name was too hard to remember). Which is better? The infix format has the familiarity of math notation but requires more button pushes involving parentheses to enter a numerical expression. RPN is stack-based; the HP calculators had a four-number stack. Instead of pushing 3 + 4 = as on an infix calculator, you pushed the sequence: 3 ENTER 4 + . The ENTER key pushed the 3 down the stack, allowing the 4 to be entered on top. Then + added the top two stack numbers and left the sum on the top of the stack, which was always displayed. After a user became familiar with these slight differences in numerical entry, the RPN calculator was more efficient, with fewer key strokes. It also was more observable with stack operation keys (shown in a closer view below) such as swapping the top two stack items (upper-left) or rolling the entire stack down (and around to the top) (upper-right).

The ENTER key was larger, as it is on a QWERTY keyboard, and used often in pushing numbers on the stack.

The display consisted of red seven-segment LED digits of small size in 14-pin DIP packages having 5 digits each. These LED arrays were also made by HP and were attractive components in themselves for small instruments, though I do not recall seeing many in other than HP calculators. Radio Shack sold them, expensively packaged, so that it was possible to replace faulty displays. However, I do not know of any display failures, though in Tektronix engineering, most engineers and many technicians had HP 35 and HP 45 calculators.

The HP 15C Legacy Continues

Time passed, and in the 1980s, LCD displays became low in cost, and having very low operating power, were well-suited for battery-powered calculators. HP’s next popular calculator for science and engineering was the LCD-based HP 15C. My over 30-year old HP 15C, shown below, finally failed; the LCD display could not restrain water vapor in the tropical humidity in which it has been in active use for at least ten years. (Neither do computer or TV LCD displays, as the seals eventually leak. It remains to be seen how large-panel LED displays persevere.)

The HP 15C became an obsolete product, but recently was re-introduced for a limited (market test?) run by HP, though at a higher price than the $150 US I paid for mine in the 1980s. (Taking dollar devaluation into account, it was still cheaper back then.) The HP 15C is in some ways an optimal calculator design for those who like RPN notation. It is minimalist: one single-line numerical display, and with only a few more functions than an ordinary engineer wants to remember how to use. It includes the Δ% function which most engineers can appreciate for tolerance calculations. The programming is easy and useful for simple formulas such as calculating two resistors in parallel. For those who like calculator programmability and are willing to spend time keying in long programs, they are retained by battery backup memory. The calculator power source is three coin cells that last for over a year in ordinary use. It was and is a great calculator.

When mine broke, I popped the lid to see if I could replace the LCD display. The battery spring had not rusted!

Alas, one large board is heat staked along the bottom to the case. If the plastic retainers are snipped to remove it, another form of attachment will be needed to reattach the board. (I have demurred, hoping that eventually I will discover how to properly disassemble it. Someone at HP from Corvallis, Oregon must know.) Note in the front photo that although the wear around the ON button is evident, the labels on the keys are as clear and legible as when the calculator was new.

For those who want an HP 15C on their computer, a virtual HP 15C emulator can be downloaded from HP here, that runs under Windows, looks identical to the hardware HP 15C and functions similarly. It might be an acceptable alternative on a hand-held computer to a separate calculator device.

The SwissMicros “HP 15C”

If you too have a broken HP 15C or want another and are in a conundrum, reticent to buy one of the more expensive limited-edition copies from HP, there is a happy alternative. A company in Switzerland, SwissMicros here, is offering a functionally identical product, shown below.

The front-panel (user interface) is identical to the HP 15C, though it includes an additional connector in the height dimension on the front, bottom-right. The size is also the same and the carrying case is very much like the HP case. The software runs on an ARM microcomputer. The user-interface differences are in the feel of the keys and the look of the display. The LCD display is inset slightly farther than in the HP 15C, and in evening desk-lamp lighting at an acute angle, I sometimes must tilt the calculator to eliminate the shadow. The numbers are somewhat more dot-quantized. These differences, however, are minor. A somewhat larger difference is that the keys have a more positive action in that they must be pressed slightly harder. This keeps “runt pushes” from spurious entry though it does require a harder push. The yellow screen-printed button functions have worn on my unit, though I learned from SwissMicros that a few units got out that had not been UV hardened, and they sent a replacement front-panel. Screenprint wear on the front-panel was a start-up glitch and is apparently no longer a problem.

The DM15L uses an internal CR2032 coin cell which can be replaced by removing the four corner screws and lifting the back cover, as shown below. Expect to replace the battery more often than with the HP 15C; it lasts about half to a third the time that the three coin cells of the HP 15C lasted. In terms of battery cost, it is about the same. The corner screws go into metal inserts and should survive many cover removals.

More product details are available from SwissMicros . Order handling was prompt and personalized; attention to delivery was exceptionally good. This calculator, especially at nearly half the price, is a worthy successor to the HP 15C – or competitor, should HP turn its reintroduction into a permanent product. The HP 15C, in whatever form, is indeed a legacy tool.

The Pocket-Sized “HP 15C”

But there is more. If you have non-large fingers, the shirt-pocket-sized DM-15 from SwissMicros costs less than the DM15L and is a miniaturized HP 15C, shown below with the HP 15C-sized DM15L and the SwissMicros cases.

The smaller calculator costs less and is well-suited for carrying around, indoors or outdoors, for it has a continuous plastic sheet on the keyboard, keeping fluids out. The keys, though smaller, have the same “clacking” action as the DM15L when pushed. The DM-15 also has a 5-pin interface connector, and it comes with a miniature carrying case made of sewn leather with a felt interior. I found it a very snug fit and use it instead as a calculator stand or dust cover on my desk. With use, it probably stretches to the right size, being leather. The smaller DM-15 has the same display type and functional performance as the larger unit.

Calculators that are Quasi-Computers

For some, more is better. Non-minimalists might be attracted to the final HP calculator to be given notice in this article, that of the HP 48G. As a next-generation calculator after the HP 15C, it has a multi-line, graphic LCD display and even more functions. Calculator users seriously desiring more functions and a computer-like “feel” in its use might be attracted to the HP 48G. Mine is shown below. Note that its LCD screen is damaged, though not by jungle vapor. I made the foolish mistake of leaving the 3 alkaline batteries in the unit while storing it in its carrying case. Chemical fumes from the batteries damaged the display. (This can also happen with camera optics or their LCD displays; remove batteries before air-tight storage.)

The HP 48G is either a computer that tries to be a calculator or else a calculator aspiring to computerdom. In either case, the functional fit in the calculator-computer spectrum seems awkward for me. The advantage of the HP 15C calculator is that it is a handy (hand-sized) and an immediate source of numeric solutions for simple to intermediate math problems which frequently occur in engineering work. It has a quite useful niche in the world of computation. The HP 48G goes beyond this functionally, and can solve more extensive problems and display graphs.

In pondering whether to invest money and self-training into a programmable-intensive calculator (whether from HP, TI, Casio, or others), the relative merits of a HP 48G versus a laptop (or smaller) computer running Mathcad or Matlab is a significant decision. Personally, I would like to see a “calculator” that runs the numeric part of Mathcad on a HP 48G with buttons that invoke a Mathcad menu tree. Perhaps Mathcad can be imported to the HP 48G and the buttons relabeled. Or maybe SwissMicros will do something like this for its high-end line of products.

In closing, I would like to know what you think

  1. about calculators generally, and about the HP 15C. Do you use one? Do you use any scientific calculator?
  2. about whether calculators like the HP 48G are too complicated or are more useful than single numeric-display calculators;
  3. and finally, whether you would buy a calculator-like device that gives you hand-held Mathcad.

11 comments on “The Calculator: An Important Engineering Tool

  1. TomC123123
    July 20, 2016

    A mostly overlooked feature of the HP48 series is that it has a built in Clock/Calendar and RS232 port.

    These features combined with the graphical display make it a reasonable clock/automated controller.

     

    TomC

  2. Koda23
    July 20, 2016

    I used an HP41CV throughout engineering school in the 1980's and still have it. It was able to print text on the display and ran short programs that were built from sequences of calculations.

    You could also assign a program to a function key, making it easy to run the program from a single key. I stored and used some routines to do calculations in dB, parallel combination of resistors, impedance calculation, etc.

  3. dspread
    July 20, 2016

    I have been using my TI-85 daily, at work and home, for approximately 20 years. It has survived numerous drops, is not glamorous, but is supremely useful, which is why it is my constant companion. On my PC I run MathCad 15 for complex or repetitive calculations, but entry on the calculator is much faster.

    I hardly ever use the graphing functions, but the 8 line text display is worth its weight in gold.

    David Spreadbury

    UK

  4. Andy_I
    July 21, 2016

    I can't find that virtual HP-15C that was mentioned.  Not at the link provided in the article.

    There are other HP-15C emulators to be found on the web, so I'm not really concerned, just pointing out an omission.

  5. Andy_I
    July 21, 2016

    I still use my HP-15C (an actual one) daily.  I probably used it two or three dozen times today.  It works like a charm, as good as new.  I don't think I have even needed to replace batteries.

  6. uberestimate
    July 21, 2016

    A calculator is not an important tool for Engineering but it is also an important tool for all Low-value business and mid value business. 

    Regards

    lyftestimate.org – Lyft Fare Estimator 

  7. Douglas.Butler
    August 3, 2016

    I own two HP15C calculators, one for my desk and one for my workshop.  I think I changed the batteries on one of them once a few years ago.  Plus I have a HP15C emulator on both my desktop and laptop computers.  I would be lost without them.

  8. Scott Elder
    August 27, 2016

    When the first smartphone came out I said that I would buy one as soon as I could get my watch, my phone, and a scientific calculator all in one package.  That happened several years ago and I have never looked back.  Now I have virtual HP calculators on my phone, tablet, and PC.

    Just stopped using blue-line quadrille pads this year.  Now I draw all rough schematics by hand on an iPad Pro with the Apple pencil using Concepts.  I move over to the fancy schematic drawing tools once I've scratched out the idea.

    Signed:  Previous owner of an HP41C and all those other powerful calculators of the past.

  9. D Feucht
    August 27, 2016

    Scott,

    Thanks for your personal example of the migration of calculators to iThings. One might suppose that calculators will soon fade out of existence, but I suspect not for the following reason: optimized user interface. The front-panel of calculators makes it easiest to calculate with them, and this endears me to the stand-alone calculator.

    For those who do algebra-driven, and hence calculator-driven, circuit design, the calculator receives a heavy workout and is justified as a dedicated device. Mine certainly continues to be.

  10. Scott Elder
    August 27, 2016

    re: fading out.

    How are virtual calculators any different from hand held calculators of old?  I think it is simply that tactile buttons are replaced with touch screen buttons.  Is there any other difference?

  11. D Feucht
    August 28, 2016

    Scott,

    “… tactile buttons are replaced with touch screen buttons.  Is there any other difference?”

    Probably not, but to me that is an important difference. When I use a calculator, I usually am not looking much at the screen while I am pressing buttons, and I rely on the tactile feedback to know that the button has been pressed. (I have a calculator that has one number button that occasionally clicks but the number is not always entered – most annoying.) 

    I suppose the solution to this is to turn on sound on the iThing for a tactile-feedback substitute. That might be quite sufficient, in which case your point is well made.

    I run the HP-15C emulator (made by HP) on my desk computer and it is very much like the real thing except for the need to click buttons with the mouse or type them in from the keyboard. The iPad is better, in putting the display and buttons close together.

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