Math Goes Mini

To illustrate the historical break-throughs in man's (and woman's) age-old struggle with numbers, we challenged a panel of experts with an everyday math problem. Namely: "If amount on line 5 is over $14,000 but under $16,000, enter on line 6 $3550 plus 39 percent of the excess over $14,000." From left to right, here are the results. Expert #1, a paleolithic cave girl, could not comprehend the problem. She forged ahead anyway and after two weeks counting on her fingers came up with an answer of 7, which was incorrect. Expert #2, fast on the abacus but not so good with English, required an interpreter. After 20 minutes, she delivered a correct answer—in yen, rather than in dollars.

Expert #3, a Radcliffe-educated engineer known as the fastest slide rule in the East, found a solution in just 20 seconds. Unhappily, the solution was incorrect. Slide rules can't add and neither can she. Expert #4, from our own Accounting Department, punched out the right answer on a mechanical adding machine in just four minutes, bloodying her finger tips in the process, since she had to use repeated addition in lieu of multiplication. The hands-down winner was expert #5 (below). Using one of the electronic minicalculators shown here, she solved the problem in a breath-taking 4.3 seconds, giving her time to relax and change into something more comfortable.

The First Pocket-Sized Electronic Calculators went on sale just two years ago. The rest is history. Almost overnight, these tiny battery-powered machines became the latest status symbol of the airborne executive. The trickle of thousands sold in 1971 grew to a torrent, and today over 50 companies compete in a market that will include literally millions of buyers this year alone. The status-conscious executive has been joined by legions of other figure freaks, in the home, on the job and in the classroom. Among students, the minicalculator is catching on so fast that some educators are already recommending that schools stop teaching multiplication and division—an idea whose time has assuredly not yet come. Besides threatening one of the three Rs, the electronic calculator has already obsoleted the slow, cumbersome and expensive mechanical calculator, as well as the less versatile mechanical adding machine. And it's well on its way toward replacing the cheaper but less accurate slide rule. Most important of all, it permits, encourages and even makes enjoyable the sort of arithmetic chores that reasonable folks have traditionally avoided.

All in all, minicalculators are a welcome reaffirmation of what's good about a technological society. They're fun to use, they're cheap, they save time, they don't take up much room, they don't pollute and they liberate you forever from the rigorous demands of long division. No question, they grow on you. People who have avoided numbers all their lives are suddenly discovering they can't live without their minis.

"As people find out how much more efficient the calculator makes them, they use it more," says Edward A. White. president of Bowmar Instrument Corporation, the firm that introduced the pocket calculator. "Calculators are addictive," he adds gleefully, and he ought to know. Just two years ago. his tiny Indiana aerospace firm was trying desperately to diversify into consumer markets. He had flown to Japan with a miniature diode display screen (the gadget that shows the numbers) developed by his researchers. He was hoping that the powerful Japanese manufacturers, whose desktop electronic office calculators had wiped out the U. S. mechanical-calculator business, would jump at the chance to buy his new display units, joining them with microminiature technology to produce a hand-held battery-operated calculator.

But the Japanese weren't buying. In one of their rare errors in the consumer-electronics business, they rejected the pocket calculator as a toy that could never sell in quantity. How wrong they were. After trying and failing to interest U. S. companies in the same proposal, White decided to build the thing himself. In September 1971, when the first hand-held calculator came on the market, it was the result of a pioneering development effort by Bowmar and Texas Instruments, one of the first companies to start mass-producing the tiny integrated-circuit "chip" that makes up the brain of the machine.

White couldn't be happier about the way calculator sales are going at Bowmar. "The Japanese have pretty well had it," he says. Never modest, he has always claimed to be the leading U. S. calculator maker. As it happens, competitors agree. They guess that he will build about one quarter of all consumer calculators made this year in the U. S. and Canada—about 1,200,000 machines. Adding to White's contentment, no doubt, is the fact that he is the largest single stockholder in a firm whose shares have gone from $6 to as high as $38 in the past 18 months.

Like the display screen, the brain of the minicalculator emerged from U. S. research laboratories in the late Sixties. A major breakthrough was the discovery of a low-cost method of producing miniature electronic circuitry. This involves what is called the large-scale integrated circuit—a calculator on a chip that packs the action of several thousand transistors into a unit smaller than a pencil eraser.

Contrary to conventional wisdom, the calculator on a chip was not a direct spin-off from the space program. Time called the pocket calculator "another hand-me-down from the aerospace programs of the Sixties," but the calculator chip and the metallic-oxide semiconductor (MOS) process that made it possible owe more to free enterprise than to Federal funding. Cynics say the spin-off story got started because NASA, in its continuing effort to justify the space program, takes credit for technological developments it had nothing to do with.

In the beginning, the calculator chip was tough to build. Early yields of usable parts amounted to less than one percent of total production. But last year, when production problems were resolved and reliable chips finally started rolling off production lines, the impact on calculator economics was dramatic. In 1971, it had taken up to five MOS circuits and four hours of hand labor to assemble the simplest model. With the calculator on a chip, the assembly time dropped to less than 15 minutes and retail prices plunged appropriately. The calculator chip is now being made by nearly a dozen semiconductor manufacturers, since no single company holds the exclusive rights to it nor to the technology. In fact, most companies in this business have cross-licensing agreements that give each of them the right to use the others' technology. This has heightened retail competition and lowered prices even further.

In fact, the competitive arena is so crowded that selecting a calculator has become as complicated as picking out stereo components. As recently as last Christmas, the decision was much easier. Nearly all the hand-held models then did the same basic job—adding, subtracting, multiplying and dividing—with only a few additional variations. But with this fall's flood of second-generation models has come an ever-widening variety of features and prices. Those who waited will find lower price tags than ever before, plus a lengthy list of options that puts even Detroit to shame.

Pocket models seem to cluster in three basic price ranges: The simplest machines—those that add, subtract, multiply and divide—cost between $60 and$70. These have accounted for the vast majority of sales to date and would have cost $100–$120 a year ago. If your primary interest is in balancing your checkbook and avoiding long division, one of these will more than fill your needs. For a few dollars more, many such machines now offer a special key to quickly calculate percentages—useful for investors and for those who do their own income taxes.

For checkbook balancers, a six-digit readout is usually adequate, since it handles numbers up to 9999.99. Anyone who has that much in his checking account can well afford a more substantial machine, but even the cheapest routinely provide eight digits, which is as much accuracy as any but the most compulsive person will ever require. Ten, 12 and even 14 digits, while available and lovely to look at, are really useful only to census takers and pure mathematicians.

A new class of $80–$120 machines is being promoted this fall by manufacturers who hope that buyers will pay more for calculators that include a memory. For many types of problems—especially the more complicated ones—a memory is worth the extra cost. But it really does nothing the user couldn't do with a cheaper machine and a pencil.

Those who won't settle for less than the best can choose from a range of special-purpose machines whose prices go from $120 to $400. These are really pocket computers, yielding answers for up to 100 types of complex math problems. They can do anything that slide rules and log tables do (and then some)—and they are quicker, more accurate and more fun, providing the cube root of your age as quickly as you punch the keys. Hewlett-Packard's HP-35, for example, can perform an almost limitless number of trigonometric, logarithmic, exponential and square-root functions—all accurate to ten digits. Its price was recently reduced to $295.

Hewlett-Packard's latest entry, the HP-45, is by far the jazziest of all hand-held calculators. In addition to doing everything the HP-35 can do, this $395 model performs all sorts of decimal-to-metric conversions—centimeters to inches, kilograms to pounds, liters to gallons, and so on. Hewlett-Packard also makes a specialized machine of interest primarily to bond salesmen. This one (Model HP-80, around $400) will give answers to any question you can ask involving relationships between time and money. Its memory even includes a 200-year calendar. And for those who are worried about bulging pockets and are willing to pay a price to avoid them, there's the Sinclair Executive, a British machine only three eïghths of an inch thick. It weighs two and a half (continued on page 248)Math Goes Mini(continued from page 142) ounces and sells for $149.95, making it almost worth its weight in gold and more than twice as expensive as the simple machines with which it competes.

Other electronic slide rules, comparable to Hewlett-Packard's original model, will come onto the market later this fall, in hopes of appealing to the back-to-school crowd, with prices starting around $200. (The cost reduction is due to simplification of circuitry.) Bowmar and Lloyd's Electronics will be among the first manufacturers to offer such models.

Pocket calculators have developed so quickly that advertising copy writers have yet to catch up. The problem is exacerbated by the fact that many pocket calculators are sold by retail department stores, whose newspaper ads read like they're written by underwear salesmen. As a consequence, vast sums of money are being spent on calculator advertisements that are either misleading or unintelligible. For the record, here is a brief glossary of pocket-calculator phraseology:

Four function: No calculator can have fewer functions, since the four are addition, subtraction, multiplication and division.

Algebraic logic: This means that problems are punched into the calculator algebraically, in the order you would do them in your head. Specifically: 2 x 3 = 6 or 24 ÷ 6 = 4. This method is easy to learn and is used by virtually all new models. Machines that don't use algebraic logic should be avoided.

Chain calculations: This simply means that you can add, subtract, multiply or divide in a series (4 x 4 = 16 - 6 = 10 ÷ 5 = 2). Again, this is something that nearly every calculator can do, so you should avoid those that don't.

Floating decimal: Almost all new pocket machines have this feature, which automatically moves the decimal point (in multiplication and division problems) to the position that produces the most exact answer the display screen can handle. Earlier models came with a fixed decimal point; this was fine for dollars-and-cents calculations but could be inaccurate when more than two decimal places were needed for an answer.

Constant factor: A button marked K locks in the first number entered—useful when you want to use the same number to multiply a series of others. For typical personal use, a constant is nice to have but far from essential.

Advertising copy is especially hazy when it comes to describing memory and percentage features. Every calculator has a memory for permanently storing the instructions that tell it what to do. But when a memory is advertised, it should mean that the result of a calculation (or a subtotal) can be stored temporarily, by pressing a button rather than writing the number down. This frees the machine for other calculations, and the stored number can be called out of the memory and used over and over again without your having to re-enter it.

The percentage key is a quick way to figure taxes, discounts, markups or other percentages automatically. To figure a seven percent tax or discount on a $100 purchase, enter 100 x 7 and then hit the percentage key. Pressing the plus key gives the total with tax ($107) and the minus key provides the discounted total ($93). For most individual uses, the percentage key is more desirable than the memory feature. Needless to say, both raise the retail price of the machine.

In fact, a calculator's price tag should reflect only one thing: what it can do. The more functions it performs, the higher the price. Unlike many other products, lower price doesn't necessarily mean lower quality. An inexpensive model doesn't work any slower or any less reliably than its higher-priced competitors. The tiny integrated circuit that is the calculator's brain is made and tested to the same specifications (most likely by the same manufacturer), no matter what the model sells for.

Still, there are two things to watch for when considering the purchase of a discount-priced machine. Given the intense competition, a few pennies can sometimes make the difference between a manufacturer's making or losing money. Designers in some instances have resorted to cheaper cases and keyboards to squeeze out those last few cents. Most keyboards have moving, or "snap-action," keys. These give a tactile feedback but are too expensive for the lowest-priced machines, many of which employ nonmoving keys. These do the job, but they don't give the response to which most people are accustomed when using a keyboard. Try before you buy.

Very low-priced models may also be close-outs. This usually means the model didn't sell, but it also could signify that a company is leaving the market, a not infrequent occurrence these days. In the latter case, a buyer would have no recourse should anything go wrong during the warranty period (usually one year) or afterward. Caveat emptor.

One of the more difficult tasks facing a buyer is choosing a company that promises to be around for a while. Many of the companies that specialize in calculators are small ones, and Wall Street observers are expecting a shakeout. So the longer you wait, the easier it should be for you to pick a winner, or at least a company that will stay in the race.

Already, a handful of companies dominate the business: Bowmar, Rapid Data, Rockwell, Commodore and Texas Instruments. These five will account for 80 percent of the total U. S. production of consumer calculators this year and two out of every three machines sold here. Large manufacturers such as Craig and Hewlett-Packard, even though their calculator sales represent only a fraction of total consumer purchases, can also be expected to endure.

For all the action the minicalculators have generated in their brief two years of existence, the next two years should be even more eventful. Prices of the cheapest models are not going to drop another 50 percent, but they will continue to soften. One knowledgeable industry executive predicts that by Christmas 1974, a simple eight-digit machine should be selling for under $50. By Christmas 1976, he sees the same device under $40. At the top of the line, he looks for more specialized applications, at comparably lower prices. As manufacturers continue to learn how to print more and more circuits on ever-smaller pieces of silicon, they can build more functions into existing hardware. Already, the same chip array that provides multiple functions for the jazzy electronic slide rules can be programmed for other specialized jobs. In the next two years, look for hand-held calculators designed for stockbrokers, machinists, students, economists, surveyors and businessmen, with price tags dropping to the $100–$250 range.

After that, who knows? The message should be clear: If you don't see a calculator that meets your needs right now, hang in there. There's bound to be one in the works, no matter who you are or what you do.