Back in the early 1960s, computers weren't for everyone. A typical computer cost hundreds of thousands of dollars, occupied several rooms or even whole buildings, and serviced a community of hundreds or thousands of users. Obtaining processing time on such a beast was a complicated administrative procedure; processor time was measured in seconds, and the cost was enormous.
At the same time, a growing number of manufacturers began to market electronic desktop calculators. Even a four-function electronic calculator could prove to be a tremendous time-saver for the scientist or accountant, often eliminating the need for using a larger computer. It was found that most calculations were repetitive; the ability to store such calculation sequences for later execution, i.e., to make a calculator programmable, became highly desirable.
Manufacturers took notice; soon, several companies, including legendary names like Wang or Hewlett-Packard, began to offer programmable desktop calculators. At a cost of several thousand dollars, these were expensive, but still orders of magnitude cheaper than a "real" computer. These calculators, in effect, were the first personal computers.
Yet calculators clearly differed from computers in many ways. A "regular" computer, even back then, had a relatively large amount of memory (measured in kilobytes) and a very fast processor capable of executing tens of thousands of instructions per second. These instructions, however, were primitive binary instructions operating on small units of data, such as 8-bit bytes. Something as simple as adding two multi-digit floating point decimal numbers required subprograms that were many hundreds of machine instructions in length. (Of course, many basic functions were provided for in the form of standard libraries, developed by the computer manufacturer.)
In contrast, programmable calculators had tiny amounts of memory (often only a few dozen bytes) and a slow processor. Calculator processors were, however, optimized for floating point calculations. Thus, a calculator might have been able to execute only a few instructions per second, but these instructions performed floating-point operations on 8, 10, or 12-digit operands. As a result, it became possible to develop fairly complex numerical applications in only a few dozen program steps.
While calculator manufacturers perfected their desktop products, manufacturers of electronic components didn't stand still either: integrated circuits of ever increasing complexity appeared on the market, making it possible to pack more calculating power in ever smaller packages at a decreasing cost. The first all-transistor electronic calculators weighed dozens of pounds and required cooling fans; in contrast, by the late 1960s, handheld calculators began to appear in stores. The development of programmable handheld calculators was an obvious next step.
This step was first taken, to the best of my knowledge, by the legendary Compucorp division of Computer Design Corporation. Their handheld programmable calculators such as the Compucorp 324G appeared as oversize pocket calculators; these beautiful instruments had all the advanced features found in many modern calculators today.
The first pocket programmable calculator was of course manufactured by the Hewlett-Packard company. The HP-65 was a stunning instrument: in a package weighing only a few ounces, it packed the power of a full scientific calculator, 100 partially merged steps of programmability, advanced programming features such as labels, subroutines, and conditional jumps, and on top of that, a magnetic card reader!
The rest, as they say, is history. Soon after the HP-65, another company, Texas Instruments, introduced its first programmable calculator, the SR-52. More sophisticated models, as well as budget calculators, began to appear in the following years. Other manufacturers also entered the race, from Britain's Clive Sinclair through Japanese giants such as Casio or Sharp all the way to Russia's Elektronika models. However, very few of these models had the same quality of design, same functional integrity, as the classic HP and TI units.
Many of the legendary manufacturers have disappeared during the price wars of the late 1970s. Many remain: Hewlett-Packard and Texas Instruments in the USA, Casio and Sharp in Japan still manufacture programmable calculators today.