Pocket scientific calculator

A shirt pocket version of a desk machine

Through the 1960s a pocket calculator could add, subtract, multiply and divide, and nothing else. Trigonometry, logarithms and exponentials still belonged to the slide rule, a marked strip of wood or plastic that students learned to read in a dedicated class and carried in a belt holster. Machines that could do the rest existed, but they sat on a desk. Hewlett-Packard's 9100A of 1968 was a desktop scientific calculator, and Bill Hewlett wanted it in a shirt pocket.

Around 1970 the HP co-founder handed that problem to France Rode, a Slovenian engineer who had joined the company in 1962 and had designed HP's first integrated circuit in house. Rode was one of four lead engineers on the project, which took about two years, roughly a million dollars and twenty engineers. The machine that emerged was built around five chips, and it reached the market in 1972.

HP's own market research had found little or no interest in a pocket scientific calculator. The company built the device for its own engineers first and only then decided to sell it.

Thirty-five keys and a reversed notation

The calculator carried no model number at first. Inside HP it was simply called The Calculator, and early units said only Hewlett-Packard on the faceplate. The number 35 came from the keyboard, a suggestion of Bill Hewlett's.

Like HP's desktop 9100A, the HP-35 evaluated expressions in reverse Polish notation rather than the algebraic order that later became standard. The user entered numbers first and the operator last, with results held on a four-register stack named x, y, z and t, plus a single memory register. The keyboard covered arithmetic, trigonometry in decimal degrees, common and natural logarithms, e to the power of x, reciprocals, square roots, powers and pi.

One detail read oddly to anyone used to later calculators: the power key was labelled x to the y, not y to the x, which made sense on a machine with no separate ten to the x key. There was also no shift key. The arc key inverted the trigonometric keys, and the first true shift key appeared on HP's later business model, the HP-80.

Fifteen digits of red light

The display was a fifteen-digit red light-emitting diode array: a ten-digit mantissa with its sign and decimal point, and a two-digit exponent with its sign. The HP-35 switched automatically between fixed and scientific notation, and its range covered about 200 decades. LED devices were dim in 1972, so the display lit one LED segment at a time rather than one digit at a time, a scheme HP research had shown the eye reads as brighter for the same power.

All of that mathematics ran on 768 bytes of ten-bit firmware, with the finished implementation taking 767 carefully chosen instructions. The calculator weighed nine ounces and measured 5.8 by 3.2 inches, said to have been sized to fit one of William Hewlett's shirt pockets. Three AA-sized nickel-cadmium cells gave about three hours of use, and owners pressed the decimal point key to leave a single junction lit and stretch the time between charges.

Sold out, and a forecast an order of magnitude wrong

The HP-35 went on sale at $395, about £165 in Britain. The forecast of 50,000 units turned out to be wrong within months: General Electric alone ordered 20,000, and HP took to warning readers of its own journal to expect waiting lists. Sales reached 100,000 in the first year and more than 300,000 by the time the model was discontinued in 1975. The price fell to $295 when the HP-45 arrived.

The hardware was built to survive its buyers: keys were moulded from two colours of plastic so the legends could not wear off, and every hand-held HP had to survive a three foot drop onto concrete, corner by corner.

The bug HP told everyone about

The accuracy of the internal algorithms exceeded that of the mainframe computers available to check them, so Dave Cochran, who led the algorithms work, fell back on manual comparisons against printed mathematical tables. In one error that survived, the natural logarithm of e raised to 2.02 returned 2 rather than 2.02.

By then 25,000 calculators had been sold, a large volume for HP at the time. In the meeting called to decide what to do about the units already in customers' hands, David Packard made the position plain: the company would tell everyone and offer a replacement rather than ship a product with a problem. Fewer than a quarter of the owners took the offer up.

The end of the slide rule

The consequences arrived fast. Slide rule holsters on student belts gave way to holsters for what people called an electronic slide rule, and colleges began dropping slide rule instruction from their curricula. Sinclair's Scientific of 1974 was a twelve-function scientific calculator at £49.95, running scientific functions on a Texas Instruments chip designed for four-function arithmetic by sacrificing speed and accuracy; by July 1976 it cost £7. HP answered from the top of the market with the HP-45, the HP-65 and its magnetic program cards.