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The HP-35 was Hewlett-Packard's first pocket calculator and the world's first scientific pocket calculator (a calculator with trigonometric and exponential functions). Like some of HP's desktop calculators, it used reverse Polish notation. Introduced at US$395, the HP-35 was available from 1972 to 1975.
Market studies had shown no market for pocket sized calculators at the anticipated price. In about 1970 HP co-founder Bill Hewlett challenged his co-workers to create a "shirt-pocket sized HP-9100". About twelve HP-35 portable calculators were made as a "hack" by and for other engineers at HP. It is rumored that the development engineer got carried away and included a full suite of scientific functions to satisfy requests from his co-workers. When these prototypes proved popular, HP decided to turn the HP-35 into a commercial product. The HP-35 was the first calculator with a full suite of trigonometric and transcendental functions.
In the first months orders were exceeding HP's expectations as to the entire market size, which was 10,000 units per year. Before the HP-35, the only practical portable devices for performing trigonometric and exponential functions were slide rules. Existing pocket calculators at the time were only four-function, i.e., they could only perform addition, subtraction, multiplication, and division. It had been originally known simply as "The Calculator", but Hewlett suggested that it be called the HP-35, because it had 35 keys.
The calculator used a traditional floating decimal display for numbers that could be displayed in that format, but automatically switched to scientific notation for other numbers. The fifteen-digit LED display was capable of displaying a ten-digit mantissa plus its sign and a decimal point and a two-digit exponent plus its sign. The display used a unique form of multiplexing, illuminating a single LED segment at a time rather than a single LED digit, because HP research had shown that this method was perceived by the human eye as brighter for equivalent power. Light emitting diodes were relatively new at the time and were much dimmer than high efficiency diodes developed in subsequent decades.
The calculator used three "AA"-sized NiCd batteries assembled into a removable proprietary battery pack. Replacement battery packs are no longer available, leaving existing HP-35 calculators to rely on AC power, or their users to rebuild the battery packs themselves using available cells. An external battery charger was available and the calculator could also run from the charger, with or without batteries installed.
The HP-35 was the start of a family of related calculators with similar mechanical packaging:
- The HP-45 added many more features, including the ability to control the output format (rather than the purely automatic format of the HP-35). It also contained an undocumented timer feature. The timer worked, but was not accurate enough to use as a stopwatch due to lack of a crystal oscillator.
- The HP-65 added programmability, with program storage on magnetic cards.
- The HP-55, a less expensive follow-on to the HP-65, provided storage for smaller programs, but didn't provide any external storage. The timer that was already present on the HP-45 was now crystal-controlled to achieve the needed accuracy and explicitly documented.
- The HP-67 expanded on the programmability of the HP-65, and added fully merged keycodes
- The HP-80 and cheaper HP-70 provided financial, rather than scientific functions, such as future value and net present value.
Follow-on calculators used varying mechanical packaging but most were operationally similar. The HP-25 was a smaller, cheaper model of a programmable scientific calculator without magnetic card reader, with features much like the HP-65. The HP-41C was a major advance in programmability and capacity, and offered CMOS memory so that programs were not lost when the calculator was switched off. It was the first calculator to offer alphanumeric capabilities for both the display and the keyboard. Four external ports below the display area allowed memory expansion (RAM modules), loading of additional programs (ROM modules) and interfacing a wide variety of peripherals including HP-IL ("HP Interface Loop"), a scaled-down version of the HPIB/GPIB/IEEE-488 instrument bus. The later HP-28C and HP-28S added much more memory and a substantially different, more powerful programming metaphor.
Calculator trivia 
- The HP-35 was 5.8 inches (150 mm) long and 3.2 inches (81 mm) wide, said to have been designed to fit into one of William Hewlett's shirt pockets.
- Is the first scientific calculator to fly in space (along with the HP-65 and HP-41) in 1972
- Is the first pocket calculator with a numeric range that covered 200 decades (10+/-100)
- The LED display power requirement was responsible for the HP-35's short battery life between charges — about three hours. To extend operating time and avoid wearing out the on/off slide switch, users would press the decimal point key to force the display to illuminate just a single LED junction.
- The HP-35 calculated arithmetic, logarithmic, and trigonomic functions but the complete implementation used only 767 carefully chosen instructions (7670 bits).
- Introduction of the HP-35 and similar scientific calculators by Texas Instruments soon thereafter signaled the demise of the slide rule as a status symbol among science and engineering students. Slide rule holsters rapidly gave way to "electronic slide rule" holsters, and colleges began to drop slide-rule classes from their curricula.
- 100,000 HP-35 calculators were sold in the first year, and over 300,000 by the time it was discontinued in 1975—3½ years after its introduction.
- In 2007 HP introduced a revised HP 35s calculator in memory of the original.
- An emulation of the HP-35 is available for the Apple iPhone and iPad.
- "HP-35 Scientific Calculator Awarded IEEE Milestone". Ieee.org. Retrieved 2012-05-17.
- $395 in 1972 ≈ $2,141.93 in 2012 (see Inflation Conversion Factors for Dollars)
- "Retro HP 35s Launched to Commemorate 35th Anniversary of First HP Handheld Calculator". Hp.com. Retrieved 2012-05-17.
- "Milestones:Development of the HP-35, the First Handheld Scientific Calculator, 1972". IEEE Global History Network. IEEE. Retrieved 4 August 2011.
- "Hewlett-Packard Calculator Firsts". H20331.www2.hp.com. Retrieved 2012-05-17.
- "HP Virtual Museum: Hewlett-Packard-35 handheld scientific calculator, 1972". Hp.com. Retrieved 2012-05-17.
- The Museum of HP Calculators' article on the HP-35
- HP Journal, June 1972
- HP-35 pictures on MyCalcDB (database about 70's and 80's pocket calculators)
- A thorough analysis of the HP-35 firmware including the Cordic algorithms and the bugs in the early ROM.
- Tom Osborne’s Story in His Own Words - the invention of the HP 9100, HP 35 and HP 65
- A list of earliest HP-35 "Red Dot" calculators