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Review: HP 35s Programmable Scientific Calculator

You may wonder what an article about Hewlett-Packard's new (2007) programmable scientific calculator is doing on a web site about historical computing devices. The main reason is that this is the first calculator produced by HP in a very long time that carries on the legacy of their earlier models. The 35s isn't a historical calculator (yet), but it is in spirit. Another reason is that I don't have a "modern computing devices" web site to put this article on.

Most modern HP scientific calculators fall into two classes: graphing and ugly. The last decent calculator made by HP was the 32sii, an RPN programmable with equation solving and integration. The follow on to this was the 33s, which took a previously nice design and made it into one of the ugliest HP calculators I've ever seen.

With the HP 35s, Hewlett-Packard has attempted to return to its roots, at least in appearance and quality. HP produced the 35s as a successor to the 33s, and at the same time as a celebration of the 35th anniversary of the very first scientific pocket calculator ever made, the HP-35.

First Impressions

An HP 35s (top centre), with an HP-67, HP-34C, HP-41CX, and HP-42S.

The HP 35s is just slightly larger in width and height than HP's earlier pocket scientific offerings, but thanks to modern technology, quite a bit thinner. It measures 6¼" × 3¼" × ¾", and weighs only 4½ ounces. The colour scheme is reminiscent of HP's classic calculators, such as the HP-19C or HP-34C, with a black keyboard bezel, sloped front keys, a double-width ENTER key, gold and blue shift keys, and a silver trim line around the keyboard and display. At the same time, the 35s has a pleasing (to me) modern look to it.

RPN vs. "Algebraic"

I think the biggest mistake that HP ever made was to name their calculators' operating methodology "Reverse Polish Notation". This makes it sound difficult, when in fact, it's easier than using an algebraic calculator. If the algebraic calculator manufacturers had called their notation "Inside-Out but Sometimes RPN", HP would probably dominate the pocket calculator market today. It is only in relatively recent times that so-called "algebraic" calculators accept input the way formulae are actually written. HP calculators have accepted input in the way that problems are actually solved since day one.

Like most of the older HPs, the 35s is an RPN (Reverse Polish Notation) calculator at heart, although it does have a well-designed algebraic mode for those who prefer this.

Power is provided by a pair of CR-2032 lithium coin cells, wired in parallel through diodes so that they can be replaced one at a time, without danger of losing any programs, equations, or data you have stored in memory,

Although not as tall as older HP keys, they have the classic sloped front, and "HP feel" when pressed.

The keyboard layout is quite good, although I have one small nit to pick, which is that the STO function is on a shifted key. As has been the norm with HP calculators for quite a while now, many of the shifted keys open menus of functions rather than having all possible functions assigned to keys of their own. As a result, the calculator has far more functions than a glance at the keyboard might suggest.

I'm happy to report that the keys have that "HP feel" that anyone who has ever used a classic HP calculator can appreciate. The keys aren't quite as tall nor move quite as far as on the classics, but the feel is there.

Functions

Most of the basic scientific functions are there, including trigonmetrics and hyperbolics and their inverses, common and natural logarithms and their inverses, squaring and square roots, arbitrary powers and roots, and conversion between degress and radians. What's missing are conversions between polar and rectangular coordinates (although there is a work-around).

The 35s also has a few built in unit conversions (°F↔°C, lb↔kg, mi↔km, and in↔cm), as well as conversion between hours/minutes/seconds (H.MS) and decimal hours (or degrees). Missing are functions for performing arithmetic directly on H.MS values.

In the statistics area, there are basic statistics on one or two variables (mean, weighted mean, and sample & population standard deviation), as well as linear regression. Also provided are factorial (which can also compute Γ), and functions for computing the number of combinations and permutations of n objects taken r at a time.

The HP 35s' display can be set to display in fixed point, scientific, or engineering notation. Handy ⇐ENG and ENG⇒ functions shifts the exponent by 3 each time when pressed, making it easy to interpret an answer like 2.345 × 10^-3 as 2,345 × 10^-6.

Vectors and Complex Numbers

In addition to working with real numbers, the HP 35s provides limited support for working with complex numbers, and 1-, 2-, and 3-element vectors of real numbers.

Complex support is limited in the sense that some very basic operations that work fine on other HP calculators like the HP-42S don't work on the 35s. For example, taking the square root of -2 yields 1.4142i on the 42S, and an error message, "SQRT(NEG)", on the 35s. Using the yx key with a 0.5 exponent doesn't work either, unless the -2 is entered as -2i0. In short, the calculator doesn't automatically switch to complex mode when needed, and even in complex mode, not all operations work (such as √x). Nevertheless, it is possible to perform complex arithmetic once you know how.

Complex numbers can be entered in either rectangular or polar form, using the i and Θ keys respectively. The calculator can be set to display results in either form as well. This is the way to work around the 35s' lack of polar↔rectangular conversions; enter the coordinates as complex number in one form, and display it in the other. One complaint about the display of polar complex numbers is that the Θ symbol looks almost exactly like the digit 8; they are only different by two pixels.

Vectors are entered using the [] key, which enters a matching pair of square brackets. The elements of the vector (if more than one) are separated by commas (gold-shifted decimal point). Vectors can be added and subtracted, multiplied or divided by a scalar, or multiplied by another vector to yield the dot product. There is no cross product function.

Logic and Other Number Bases

There are two menu keys, BASE and LOGIC, for entering and manipulating numbers in binary, octal, and hexadecimal. The base in which they are displayed is independent of the base in which they are entered, so it is always necessary to add b, o, or h after non-decimal numbers when entering them. However, the calculator must be in hexadecimal display mode to allow entry of the digits A through F (which is done with the six keys in the row above the ENTER key, which have alpha labels H through M). The logic menu contains AND, OR, XOR, NOT, NAND, and NOR functions.

	The HP 35s can work in fractions, which I find useful in the workshop.

One feature of the 35s that I really like is its ability to work in fractions, which comes in really handy in the workshop. The calculator can display fractions with denominators up to 4095, and can be set to always choose denominators satisfying certain requirements (for example, a power of 2 when working with inches). Unfortunately, the interface for these special settings is a bit awkward, requiring the setting of flags.

Memories

In addition to the twenty six named memories, there are 801 numbered memories. To access these, first store the desired number into named memory I or J, and then use STO or RCL together with the (I) or (J) keys. This sounds awkward, and it is, but it is a feature that is invaluable for programming.

Every memory in the HP 35s, both the named and numbered ones, can hold either a single real number, a complex number, or a vector of real numbers.

Equations, Solve, and Integrate

Like its immediate predecessors (HP 33s and 32sii), the HP 35s has an equation mode where equations and formulae can be entered in a one-dimensional algebraic syntax (like in C, Pascal, BASIC, FORTRAN, etc.). Such equations can be used as formulae, in which case the calculator prompts for values of all the variables and then computes the answer (and assigning it to the lone variable on the left hand side of the equals sign, if any).

Alternatively, the equations can be used together with the calculator's powerful solve and integrate features. In case you've been living under a Casio or TI rock, solve and integrate first appeared in the ground breaking HP-34C introduced in 1979. These functions can solve an equation for an unknown variable, or numerically integrate a formula over a specified range. In the HP-34C the equation or formula had to be expressed as a program, but in later calculators such as the 35s, it can be written in the above-mentioned algebraic form. Furthermore, if the equation or formula has more than one variable, you can specify which one you want to solve for or integrate over, and the calculator will prompt you for values of the other variables (which are then treated as constants).

Equations, solve, and integrate are probably the three most powerful aspects of the 35s if you don't want to write programs. With these features, you can solve a lot of problems that might otherwise require programming.

Programming the 35s

Ever since my first one (a Commodore PR-100), I can't work without a programmable calculator. Like HP programmables of days gone by, a simple HP 35s program is basically just the same sequence of keystrokes that you would use to solve the problem by hand. Once entered, you can solve the same problem over and over for different inputs without having to perform the operations yourself.

Two lines of an HP 35s program to compute the area of a circle.

Of course, if that's all there were to programming, there wouldn't be much to say about it. However, there's a lot more. The simple "same sequence of keystrokes you'd use to solve the problem manually" type of program can be augmented by looping, conditional tests, and branching. This means that the calculator can perform repetitive operations, make decisions, and perform alternative calculations while computing the answer to a problem, just like a full-blown computer.

The HP 35s provides many powerful programming features, including a complete set of x versus y comparison tests (and the corresponding x versus zero tests), both label and line number based branching (which is good, since there are only 26 labels), subroutines (up to 20 levels deep), and looping constructs.

Although many programs can be written to take all their inputs at the beginning (on the four-level RPN stack), programs can also pause and prompt for additional input while the program is running. Likewise, instead of just returning one answer at the end, they can display messages and intermediate results before the program completes.

There are about 30,000 bytes of program memory in the HP 35s, which is approximately enough for 10,000 program steps. This memory is shared with the 801 numbered memories, so as the memory fills up with programs, the number of available memories decreases.

The calculator can hold more than one program at a time, each program being named by a single letter label, and executed by pressing XEQ A ENTER (replace "A" by the desired letter).

If you want to get some idea of the kind of sophisticated programs that can be written, please see my Curve Fitting and Matrix Multi-tool programs for the HP 35s. These programs make use of many of the HP 35s' programming features including comparisons, looping, subroutines, indirect memory addressing, message display, and data input and output. One doesn't have to write programs as sophisticated as these to take advantage of the 35s, but the power is there when it's needed.

The one shortcoming of the 35s (and HP's other programmable non-graphing calculators after the HP-41C series with its optional magnetic card or tape storage), is that there is no way to save programs outside of the calculator other than writing them down. There is no printer output, removable memory card, or PC connectivity. However, the calculator does retain its programs when turned off, and the dual battery feature lets you replace the batteries without risk of clearing the memory. The only way you can accidentally lose the programs is if you let the batteries run down, or the calculator malfunctions.

	The manual is good, but I had mine spiral bound to make it easier to use.

The Manual

The 200 page manual is quite good, being printed in two colours and reasonably thoroughly covering almost every feature of the calculator. There are a few errors, which appear to have crept in because the manual was derived from that of the HP 33s, with which it shared some, but not all, features. In order to make the manual a bit easier to use at my desk, I had the local Kinkos shop cut off the square binding and then spiral bind it. This lets it lay flat while open to any page (most earlier HP manuals came bound this way).

[January 2008 Update: Recent purchasers have discovered that the calculator now comes with only a 24-page printed getting started guide and a CD containing the main manual in PDF format. Although I'd like to have a PDF version of the manual for use as a reference, I prefer the paper version for just sitting down and learning all about the calculator.]

Conclusion

Does the HP 35s live up to what one would expect from a 35th anniversary offering from the company that invented the scientific calculator, and once made the best such gadgets on the market?

It comes pretty darn close! There are a few quirks in both appearance and functionality, but it is a step in the right direction. It looks like an HP calculator, it feels like an HP calculator, and it mostly works like an HP calculator ought to. Whether this is a promising sign of things to come from HP, or a last stand, remains to be seen.

The HP 35s comes pretty close to the look and feel of HP's calculators of days gone by.

The programmable calculator occupies an ever narrowing niche. Most problems can be solved using a simple (possibly scientific) calculator, and those that can't are usually done on the now ubiquitous computer. Higher-end graphing calculators, although somewhat harder to learn to use, can often solve the in-between problems without the user having to resort to programming. On the other hand, a programmable calculator works like an ordinary calculator, making it ideal for day-to-day use, but with the programming capability there when a complex or repetitive task presents itself.

I am of course a collector of historical HP calculators, but I'm glad I bought my HP 35s. It is a calculator I actually use, and so far, it has proven itself worthy of the Hewlett-Packard name.

The HP 35s is available from many college and university bookstores (I bought mine at the York University bookstore in Toronto), or on-line from Amazon.com.
 
 

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Last updated Saturday April 12, 2008.	E-mail Stefan
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