Wang LOCI-2

The Wang LOCI-2 (with LOCI pronounced "low-sigh") calculator is of major historical significance, partly due to the rather amazing capabilities for its time, and also due to its use in a number of historic applications, including its use as a controller for testing space suits under development for NASA's historical Apollo moon-landing missions. The LOCI-2 was an improved version of Wang's first marketed electronic calculator, the LOCI-1.

Early Wang LOCI-1 Calculator

The LOCI-1 was introduced in the fall of 1964 at a price of $2,750. The LOCI-1 was quickly followed up by an improved version of the machine called the LOCI-2. With only a few months of time on the market before the LOCI-2 came out, the LOCI-1, was quickly rendered rather irrelevant by the introduction of the LOCI-2, leading to the quick discontinuation of the LOCI-1. (NOTE: If you know of the existence of a LOCI-1 calculator in any condition, please contact the Old Calculator Museum, as the museum would be very interested in speaking to its owner concering acquring the calcualtor for the museum's collection.) In July of '65, Wang Laboratories announced the LOCI-2A model, which added three more banks of four core memory-based storage registers to the calculator. The LOCI-2A thus had the capacity of 16 memory registers. Each memory register could hold a single number including sign and floating decimal point location. The introduction of the LOCI-2A pretty much sidelined the original LOCI-2 model, as the additional twelve storage registers provided by the LOCI-2A model made more complex operations possible, as well as making programming much easier.

The museum currently has two Wang LOCI-2 Systems in its collection; a Model 2A (Option A adds three more banks of four memory registers to the single bank of four memory registers on the base LOCI-2), and a Model 2AD, (Option D adds a special output interface card to allow connection of an external printer) with the external Wang LOCI Printer peripheral.

The thing that made Wang Labs' LOCI calculators so ground-breaking was that they could perform advanced math operations with a single key-press that no other electronic calculator on the market at the time, nor for quite some time thereafter, could do, and, it performed the these calculations in less than 1/10th of a second. The magic that the LOCI brought to the table was the unique ability to calculate logarithms and anti-logarithms entirely automatically, with a single key-press. Logarithms are a mainstay of many scientific, physics, and engineering calculations, and the fact that the LOCI calculators could generate logarithms and anti-logarithms in mere milliseconds was profound. Dr. Wang had invented a relatively simple arrangement of digital logic that used successive addition and subtraction of a set of constants contained in a read-only memory (made with diodes) that would generate the natural (base e) logarithm or anti-logarithm of the supplied argument. The logic to implement the function was not that complicated, and relied on the fact that any electronic calculator has to have the ability to add and subtract as its core functionality, so all that was really needed was some simple counters and state logic to sequence the in-built addition/subtraction functions through the log/anti-log generation process. Other programmable electronic calculators on the market at the time, such as the Mathatronics Mathatron, Wyle Laboratories Scientific, or even the amazing Olivetti Programma 101, could be programmed to calculate logarithms, but it would take the logarithm program on these machines orders of magnitude longer to calculate a single logarithm of a number. The ability of Wang Labs' LOCI calculators to generate logs and anti-logs with a touch of a key, (as well as one-key square root and squaring and reciprocal functions of both (e.g., 1/√x and 1/x²), all of which were facilitated through the use of the logarithm functionality), the high speed of these functions, along with the programmability and memory register capabilities of the LOCI-2 models, made the machines big winners in the high-end electronic calculator marketplace. The LOCI-2, although rather expensive, began selling lot hotcakes into engineering, laboratory, research, and university environments. The calculators literally sold themselves when shown at trade shows, and the success of the LOCI calculators began a period of explosive growth for Wang Laboratories.

Space-Suit Testing System Based on Wang LOCI-2, Custom Built for NASA by Wang Labs Systems Division
Photograph Courtesy Frank Trantanella

In just under a year, the LOCI calculators ended up being eclipsed by Wang Labs' 300-series calculators, which were announced in late 1964 (Note the italicized "announced" - Wang Labs had a habit of announcing calculators significantly before they were able to be delivered to customers). As the LOCI's technology aged, the focus for it shifted to marketing the calculators as a "desktop computer" rather than a calculator, in an attempt to continue the machine's marketability. One aspect of the LOCI-2 was that it could be rather easily interfaced to external electronics, allowing it to serve as a controller for larger system that needed some "intelligence" as part of its operation, a role the LOCI-2 could serve with appropriate interfacing and programming. Part of the reason behind this marketing re-classification of the LOCI-2 was that the 300-series ended up being such a tremendous success for Wang Labs that Dr. Wang didn't want the 300-series' success diluted by "competition" from the LOCI-2, even though the LOCI-2 was already a technically outdated product. Changing the focus for marketing the LOCI-2 as a computer (which they really weren't, but this was marketing-speak) allowed the LOCI-2 calculator to continue to sell within the low-end of the computer market segment, while freeing up opportunities for the new 300-Series calculators in areas where the LOCI-2 wasn't so applicable. This change of marketing tactics led the LOCI-2's marketing and sales to be targeted toward environments where programmable control was needed. In fact, Dr. Wang assigned one of his key engineers, Frank Trantanella, to the position of Vice-President of Systems Development, a group chartered with designing custom systems that used the LOCI-2 as the controller in diverse applications such as steel mill controls and Apollo-program space suit life-support system testing.

The development of the LOCI is a very interesting story that I'll go into in some detail before getting into the technical side of this wonderful calculator.

Dr. An Wang, founder of Wang Laboratories

Performing mathematical calculations with digital electronics was always a big interest of Dr. An Wang, the founding father and engineering genius behind Wang Laboratories. In his college years at Harvard, Wang worked side-by-side with Dr. Howard Aiken, one of the pioneers in computing technology. After receiving a PhD in applied physics from Harvard, the now Dr. Wang was hired on as a research fellow in the Computation Lab at Harvard. Dr. Wang was assigned to work on solving problems with newly-developed magnetic core logic technology. This technology involved the use of ferromagnetic material forms of various shapes (typically rings) with wire windings or wires passing through them that could be interconnected to perform logic operations. This logic technology had potential practical use in military systems because of its resistance to electromagnetic pulses that occur when nuclear weapons are detonated. In the end, this ferromagnetic logic technology never really went anywhere, but Dr. Wang came up with the idea of using the ferromagnetic rings as storage elements, creating chains of the rings interconnected in such a way that they became a shift-register. A shift registers is a circuit capable of storing as many binary bits as there are storage elements in the register. The bits in the storage elements can be shifted left and right by pulses, and the register can also be loaded with an arbitrary binary pattern in parallel, as well as read out in parallel, or serially by observing the output of the first or last stage of the shift register as shift pulses are applied. The notion of implementing a storage register, a function that is a requirement of any kind of calculating machine, triggered the thought that perhaps a somewhat different arrangement of the magnetic rings could be used effectively as a memory system for a calculator or computer, storing the equivalent of many "registers" worth of binary numbers. The thought also occurred that rather than accessing the information in the storage serially, perhaps the rings (cores) could be arranged in a two or three-dimensional method to allow random access to any individual bit within the memory, whereas with the shift register, in order to observe the state of a given bit, the system had to shift the bits in the register until the desired bit was at one end or the other of the register in order to be read out. The shifting necessary to move a desired bit to a point where it could be accessed required time - time which was wasted just waiting as the bits shifted around in the register. A random-access memory, where any given bit can be accessed directly, could be considerably faster, less complex to address, and in theory less-complex electronically than shift-register storage. Dr. Wang began work on implementing a memory system using these magnetic cores, and in time developed a system by which arrays of the cores were strung on thin wires arranged in an X-Y grid. Through applying specifically shaped and timed current pulses through the wires, any single core could have the direction of its magnetism changed, such that the direction of the magnetic field in the core was clockwise or counter-clockwise. A wire was also threaded through all of the cores, in which a tiny current would be generated when any core in the array changed its magnetic state. By this method, it was possible to sense the state of any of the cores by simply selecting the appropriate wires that intersect at the core that contains the desired bit, and monitoring the state of the sense wire. The problem with this method that the act of sensing the state of a core requires that the core change its state, effectively "forgetting" the previous state. Dr. Wang's solution to this problem was to simply add an additional cycle to write the original state of the core back into it, thus returning it to its original state.

It is worthwhile to explain the general theory of operation of magnetic core memory here, as many other calculators in the museum utilize this technology for implementing the working and memory registers of the machines. Since the LOCI-2 is one of the earlier electronic calculators to utilize core memory technology, this seems as good a place as any to go over the theory of how it works. Core memory is generally laid out in a two-dimensional plane, with horizontal wires and vertical wires arranged in an array, with a toroidial core (donut-shaped) of ferromagnetic material woven into the wires such that each core is at the intersection of one horizontal wire, and one vertical wire. The magnetic cores can be induced to hold a magnetic field that is oriented either in a clockwise or counter-clockwise direction within the core. There is no "in between" state, a core is either magnetized in a clockwise or counter-clockwise direction.

For example, let us say that a magnetic core magnetized in a clockwise direction is defined as a "1". Obviously, then the same core magnetized in a counter-clockwise direction would represent "0". Let us assume that a given core is currently storing a "1", e.g., it is magnetized in a clockwise direction. Sending a short pulse of 1/2 of the current necessary to force a core to a "1" state through the horizontal wire passing through the core to be read, and the same 1/2 current passed through the vertical wire that passes through the same core will result in a full current being seen by the selected core at the intersection of the horizontal and vertical wires, with all other cores on the wires seeing only 1/2 the current needed to change their state. Because the other cores only see 1/2 the current necessary to change their state, they remain as they were. The single selected core, due to the full current at the intersection of the horizontal and vertical wires, will be forced into being magnetized in a clockwise direction, or into the "1" state. Since we said that the core is already magnetized in a clockwise direction, the sense wire that winds its way through all of the cores in the array would see no change in the state of any of the cores, and from that, the fact that the core contained a "1" can be inferred due to no pulse on the sense wire. That fact is temporarily stored in a single flip-flop register for noting the state of the core before the operation occurred.

If the selected core was instead magnetized in a counter-clockwise state, e.g., storing a "0", when the core is selected, it would switch state from being magnetized counter-clockwise to clockwise as a result of the intersection of currents in the wires going through the core creating a sufficient magnetic field to flip the direction of magnetism of the core. When that magnetic field "flip" occurs, a a small pulse is generated in the sense wire, which is amplified and fed into the temporary flip-flop to note than the core was in a "0" state. However, now the core is magnetized in the clockwise direction, which is not what we want - we want the core to retain its '0' state after being read. The flip-flop stores the state of the core before the change, so the state of the flip flop can be used to return the core to its original '0' state.

The state of the temporary flip-flop is referred to, and currents as needed to put the core back to its initial direction of magnetism are generated based on the stored status in the flip flop, and the core is set back to being a "1" if the flip flop contains a 1, or a "0" if the flip flip contains a 0. With the core restored to its original state, the flip-flip can be referred to by other circuitry to determine was is stored in that particular core. The entire operation of reading the state of a given core and restoring it to its read state can be performed in a matter of a few microseconds (millionths of a second), making magnetic core memory much faster than shift register or delay line storage, and the fact that it can be accessed at random without having to wait for circulating or rotating type memories to position the desired bit to a point where it can be read or written, makes magnetic core vastly superior to these other storage technologies. Remember, at the time the LOCI calculators were made, the integrated circuit was in its very infancy, with an IC containing a couple of logic gates or a flip flop or two, and were profoundly expensive. There was no such thing as a RAM chip like in today's computers. At the time, magnetic core memory was the top-of-the-hill high-speed, high volume memory technology, and it was all started by Dr. An Wang.

A special characteristic about magnetic core memory is that power is only required to change the state of cores (both writing and reading), and when the memory is not being accessed, the state of the core array remains, even if the power to the device is turned off. The content of the magnetic core memory will remain in its state technically forever, with the only possibility of data loss being a large magnetic field that could potentially have enough strength to change the state of the cores. Programs and data in old computers that use magnetic core as their main memory have been recovered many years after the computers had been turned off and retired. When the old machines were dusted off and checked out to make sure they were still electronically sound, the content of the core memory could be read out, with all the data stored within the machine being able to be recovered after decades of disuse.

Magnetic core memory revolutionized the means by which computers would implement their main memory. Prior to the existence of magnetic core memory, computers had to use rotating magnetic drums and disks, mercury, wire, or crystalline-based delay lines, or temperamental electrostatic storage tube main-memory technologies, all of which were slow, fussy to implement, had limited storage capacity, and were all physically quite large. Magnetic core memory changed all of that, allowing for the fast and reliable storage and recall of hundreds of bits of data in an area the size of a small Post-It® note.

Dr. Wang's memory concept worked so well that a patent was applied for and granted to Dr. Wang for his developments in magnetic core logic and storage principles. The patent was applied for on October 21st, 1949, and was granted as US Patent #2709722 on May 17, 1955. That patent would prove to be both a blessing for Wang Laboratories, and a curse for Dr. Wang.

After working at the Harvard Computation Lab for a few years, Dr. Wang had saved enough money to start his own business. In 1951, he resigned his role at the Computation Lab and opened up Wang Laboratories with his long-time friend Dr. G. Y. Chu, as the first employee. Wang Laboratories specialty was to digital electronics. Early on in the history of Wang Labs, Dr. Wang's interest in digital circuits led his company to develop digital electronic "building blocks" that could be wired together to make all kinds of digital systems. The building blocks took the form of transistorized circuit boards, each of which had a specific function, for example, six two-input AND gates, or four JK-type flip flops. The printed circuit boards had edge-connector fingers that would bring the various signals that go into and out of the logic elements on the board, as well as providing connections to the necessary power-supply voltages. The boards used standardized power supply voltages and logic levels so that it was easy to interconnect the logic elements together to form complex systems.

Wang Labs offered standard chassis components with a built-in power supply, and varying numbers of edge connector socket slots (that were pre-wired to the standard power supply voltages) that the logic boards could plug into. By interconnecting the various logic modules, all kinds of digital systems could be constructed. A number of modules could be combined using a magnetic core array to provide a memory for these logic systems, all implemented in standardized circuit cards, with the core array also carried on a circuit card. At the time, there was little competition in this area of electronics, as most digital electronic systems were highly complex computers that required "ground up" design and minimization of components to keep costs under control. That meant that many computers of the era used their own standard logic circuit boards, but they were heavily customized to the specific needs of the computer system. Wang Labs' generalized circuits could technically be used to build a full-blown computer, but it would have been prohibitively expensive to do so. However, for smaller-scale logic systems such as process-control, sophisticated security systems, and machine tool controls, Wang Labs' system was perfect for building prototypes which would then be re-implemented using more cost-effective construction methods once the bugs were all worked out, or, in the case of smaller systems, the system manufactured using Wang's system and embedded as the control in the product.

Profile View of LOCI-2

Wang Labs also offered electronic system design services, where a company could provide specifications for a system they needed built, and Wang Labs would custom build the system using their standard logic modules. Wang Labs did a brisk business selling the logic modules and chassis, as well as custom design of customer logic into a functional system. While this business sustained Wang Labs reasonably well, Dr. Wang had visions of doing much more. But, his visions would cost money, and while the company was making a profit, investing in Dr. Wang's ideas would cost more than the company could afford.

This situation changed when Chicago-based Warner Swasey showed up, with a keen interest in automating the machine tools that they manufactured. These machines were operated by hand by skilled machinists, and Warner Swasey engineers know that the technology existed to allow the machines to be electronically controlled to replicate the manipulation of the machine's controls just as skillfully as a machinist, but do so the same every time, and never get bored, need a bathroom break, or a vacation. The problem that Warner Swasey had is that they did not have the electronic engineering talent within the company do create such a control system.

Warner Swasey was a major player in the business of manufacturing machining equipment such as lathes and milling machines for machining raw metal into high-precision parts. Warner Swasey came to Wang Laboratories seeking the electronics expertise of Wang Labs to make control units that would automate the operation of their machining equipment. The idea was that the control unit could be connected to precision servo motors or stepper motors to operate the machine's controls, as well as motor speed controls to control the rotation speed of a part in a lathe, or the speed of a metal machining tool in a mill. The control could also get feedback from sensors on the machine equipment to make sure that the machine was properly being controlled by the system. With such a system, the all the machinist had to do was load metal stock into the machine, start the controller's cycle, watch over the machine while it ran, remove the finished part when the cycle was completed and put a new blank in and start the machine again, and perform various checks and clean-up (de-burring) of the completed part while the next part was being automatically machined.

Warner Swasey management felt that Wang's logic module technology was particularly well-suited to develop a controller for their machining equipment. A proposal was put together whereby Warner Swasey provided a sizable infusion of capital to Wang Labs in return for a share in ownership of the company. Wang Labs' engineering team fairly quickly put together a prototype machine controller that read a program from a punched paper tape to direct the operation of a Warner Swasey lathe. Instructions punched on the tape would control the speed of the lathe's spindle, as well as the X and Y position of the machine tool. Other instructions could select one of a number of different machine tools to be used in the various operations necessary to create the part. Through a series a steps punched on the tape, a complex part could be turned from a bare piece of bar stock. At the completion of the part, an instruction will direct the machine to come to a stop, and the punched tape would rewind to the beginning of the program, ready for the operator to press the START button on the console to begin working on the next part.

As part of the deal, Warner Swasey was given all of the information on the design and construction of the prototype controller, and they ran with it, building their own numerical control systems for their machining equipment, using Wang Labs chassis and logic modules to build them. So, Wang Labs won double with the deal; they had on-going revenue from the sale of a lot of logic modules and chassis components to Warner Swasey, and also got a nice chunk of cash from them in terms of investment. Dr. Wang had plans for the money that Wang Labs received, but those plans wouldn't be able to materialize right away. Fortunately for Wang Labs, the Warner Swasey money turned out to contribute to saving the company from potential ruin.

Wang/Compugraphic Linasec

In the early 1960's, Wang Laboratories had used its electronics expertise and its logic module technology to develop what essentially was a very early electronic word processing machine (quite some time before the term "word processor" was coined) for a company called Compugraphic. The system they designed and built for Compugraphic was a machine that was called Linasec. Linasec was a machine that would take raw text input from punched paper tape, and, with some assistance from a human operator, perform proper spacing to justify the text into even-margined columns, punching the resulting justified text onto another paper tape which would feed a hot-slug typesetting machine. Compugraphic's goal for the Linasec machine was to speed the process of turning news reports coming off of wire-service teletypewriters (which punched the text onto punched paper tape) into justified text ready for printing, especially for newspapers. The name Linasec came from the fact that the machine could perform the justification operation at about one line of text per second, e.g., one LINe A SECond. Prior to this machine, the justification operation was a slow and laborious operation carried out by the the typesetting machine operator, manually inserting spacing and hyphenation of the text to properly justify each line of text. Wang's engineers developed a system that was quite easy to use, performed the job admirably and much faster than manual justification, and cost significantly less than any other text justifying system on the market at the time. By 1964, sales of the Linasec machine helped grow Wang Laboratories to a $1-million plus dollar (in sales volume) company. At around the same time that Wang Labs was riding high by crossing the magical $1M sales figure, Compugraphic threw a monkey-wrench into the works. They decided to quit selling the Wang-built Linasec. Compugraphic opted to manufacture and sell their own version of Wang's design. Contractually, Compugraphic owned the design, and even though Wang Labs had actually designed and built the machine, there wasn't any language in the contract that stipulated that Wang Labs had exclusive manufacturing rights to the machine. There wasn't anything that Wang Labs could do but step aside and let Compugraphic go their own way. Wang Labs' Linasec manufacturing business had become a crucial revenue stream for the company, and the instantaneous loss of this business had pretty serious financial implications for the company.

While the situation was rather traumatic, Dr. Wang was not one to let this setback get to him. His mind was always working, and to his credit, he had ideas in mind that in less time than one might imagine, would more than make up for the loss of the revenue provided by Linasec. Dr. Wang's Ace-in-the-Hole? An all-electronic calculating machine called LOCI.

Because of the loss of the business provided by production of Linasec for Compugraphic, Dr. Wang had to come up with something quickly to replace the lost revenue stream. The time was right for Dr. Wang to bring his calculator ideas to life. Fortunately, before the Compugraphic fiasco occurred, some of the money from the Warner Swasey deal had been allocated to start up a research project to begin looking into development of an electronic calculating machine. Dr. Wang hand-picked the people involved in this project from his best digital design engineers who had done work on Wang's custom digital systems design projects, as well as those involved in the development of WEDILOG and Linasec. With this research already underway, Dr. Wang himself got personally involved with the project, working side-by-side with his carefully chosen group of engineers. The team put in long-hours working tirelessly to bring the calculator to reality. Two key players were Prentice Robinson and Stan Zlatev, team-lead engineers who were responsible for taking the concepts developed by the research project, and turn them into a tangible design that Wang Labs could bring to market in short-order. The primary design goals were for a calculator that would be an invaluable tool for engineers and scientists that could quickly and accurately perform the four basic math functions, along with high-level operations like square root, logarithms, and exponential calculations.

The problem with building a calculator that could do scientific calculations back in 1964 when this development work was going on is that the only choice of component to build digital electronics was the discrete transistor. While transistors were a huge advance over vacuum and cold cathode tube technology like that used in the revolutionary Sumlock Comptometer ANITA Mark 8 calculator, it took a lot of transistors to build digital circuits that could do more than just the four basic math functions. At the time, the number of transistorized electronic calculators on the market could be counted on two hands. The few available all-transistor calculators took up the majority of a desktop and could only add, subtract, multiply, and divide. These calculators were made by Friden(US), Canon(Japan), Sharp(Japan) and IME(Italy). Friden also had introduced a calculator (the Friden 132) that could calculate square roots automatically, but was not programmable. A few other manufacturers (Wyle Laboratories, Mathatronics, and Monroe) had either introduced or were soon to introduce their advanced calculators that had the ability to be programmed, allowing for higher-level math to be implemented by writing programs to perform calculations such as generating logarithms. The problem with these advanced calculators was that they were slow, taking seconds to calculate a logarithm. Dr. Wang wanted his calculator to provide answers to complex operations like logarithms measured in milliseconds (1 millisecond = 1/1000th of a second).

Among these advanced calculators was the Monroe EPIC-2000, which consisted of a small suitcase-sized electronics package that was connected to a desktop keyboard/printer unit that was about the size of an electromechanical desktop printing calculator, with a thick cable connecting it to the electronics package . A program for the EPIC-2000 (which allowed only to generate a natural logarithm would take a few seconds to return a result.

Another advanced electronic calculator available during this time were the Wyle Laboratories WS-01/WS-02 calculators. The WS-01 used a rotating magnetic drum for its memory(which proved to be terribly unreliable, and was replaced by the WS-02 that ditched the rotating memory in favor of a magnetostrictive delay line storage system. Both machines were otherwise functionally identical. The Wyle Labs calculators provided three memory registers and could perform automatic square root, along with the usual addition, subtraction, multiplication, and division. The machine had an astounding capacity of 24 digits, with fixed decimal point user-selected anywhere from thirteen to zero digits behind the decimal point. Optionally, the WS-01/WS-02 calculators could be equipped with a unique punched card transport that would read punched cards taped together in forward or reverse directions to allow branching and looping operations (with cards taped into a loop, which could obviously become a bit unwieldy with a long, complex iterative program). While the Wyle Labs calculators were reasonably fast, when coded as program steps onto punched cards, the process of moving, reading, and interpreting the punched cards was quite slow. Branching and looping operations could require that quite a number of cards be "skipped over" in order to find the correct next instruction, with the calculator having to wait for the seeking operation to complete. To get the best performance out of iterative programs, the programs would have to be very carefully coded to minimize the amount of skipping over of instructions, which made the programming rather tedious. A natural logarithm function programmed to be as efficient as possible would take a up to seven seconds to return a result. The result was arguably considerably more accurate than a slide rule, but one could get a good approximation with a slide rule in half that time. Looking up the logarithm in a book might take just about as long, and the answer was generally not quite as accurate, but the book cost over two orders of magnitude less than the $4,350 Wyle Labs WS-02 equipped with the punched card reader.

The most advanced calculator of the time was from a relatively obscure company called Mathatronics. The company was formed in early 1962 specifically to develop an advanced electronic calculator that was more like a desktop computer than a calculator, and though largely successful at achieving the goal, never really became a major force in the calculator market. The Mathatronics 8-48 calculator was a a huge machine, weighing roughly 80 pounds, that offered advanced math operations consisting of pre-wired (wire-rope magnetic ROM) advanced math operations, full algebraic equation input including evaluation using the mathematical rules of precedence, eight memory registers, and learn-mode programmability of up to 48 steps. Certain models of the machine had a logarithm program pre-wired into the machine (as in the example exhibited here). The time it took to calculate a logarithm was was measured in seconds. Unfortunately, the pre-programmed functions of the first-generation Mathatron calculators could not not be executed from within a user-written program, and were only available from the keyboard.

Dr. Wang's contribution to LOCI project was his invention of a relatively simple system of logic that could generate logarithms and anti-logarithms through the systematic addition and subtraction of a series of hard-coded constants stored in read-only memory from the number to be processed. Since any calculator, at its base level, had to be able to add and subtract. Without these basic math functions, multiplication and division could be added by using repeated addition and subtraction. Addition and subtraction were the fastest math operations that an electronic calculator could perform, so using those operations as the basis for calculating a logarithm made the procedure very fast. With the logic for addition and subtraction already in place, only a small amount of sequencing logic, a read-only memory that stored the various constants used to calculate the logarithm, and a special register that accumulated the logarithm as the process ran, were needed to add the logarithm function. The design of the circuitry was optimized to allow the procedure to run as quickly as possible, utilizing registers that were fully electronic (no rotating memory, delay lines, or even magnetic core). While this type of design was more expensive to implement, the benefits as far as the performance of the calculator made up for it. This circuit would form the foundation of the calculator that would catapult Wang Labs out of the doldrums created by the loss of the Compugraphic Linasec business, making Wang Laboratories one of the rising stars in the electronics industry of the late '60's and early '70's.

An interesting side-note to this story is a quotation regarding the Wang LOCI calculators from a document (Electronic Calculators Report, 1965) published in 1965 by Friden, a leader in the mechanical and early electronic calculator marketplace. The quotation states: "Wang Laboratories is a very small company and we do not expect them to be a serious factor in the desk calculator market". It's clear that the authors of this report at Friden had no clue of the the future powerhouse that Wang Laboratories would become in the calculator marketplace, creating calculators that Friden simply could not match until years later.

Model/Serial Number Tag on LOCI-2 (Rear Panel)

A prototype LOCI (which, by the way, stands for LOgarithmic Computing Instrument) was built as a proof-of-concept. This original LOCI, made out of Wang's own "Logi-Bloc" circuit module product (this prototype appears to have been lost to time, as no sign of its existence has come to light), set the stage for Wang's first production calculator, the LOCI-1, formally introduced in September of 1964 with an initial sales price of $2,750. Within a couple of months, the price for the LOCI-1 was reduced to $2,500 in preparation for the introduction of a new, even more powerful Wang Labs calculator.

The LOCI-1 could add, subtract, multiply, and divide, as well as generate natural logarithms (with roughly eight digits of accuracy, far better accuracy than any slide-rule could provide, and at least equal in accuracy to logarithm tables printed in books), as well as performing an anti-logarithm calculation with a single keystroke. The LOCI-1 also performed one-key squaring and square root, along with the unusual inclusion of single-key calculations of the reciprocal of the square of a number (1/x²), and the reciprocal of the square root of a number (1/√x). With the LOCI-1 able to perform these functions with a single key-press, yielding a result in milliseconds was truly mind-blowing at the time. There was nothing anywhere that could do this that sat on a desktop and plugged into a regular power outlet, and was within the budget of just about any engineering, scientific, or laboratory organization. The only way to perform these types of calculations prior to the existence of the LOCI-1 was to work out the results by-hand, using logarithm tables in book form, or a through the use of a slide-rule(which had accuracy limited to perhaps two or three places behind the decimal point at best) and a mechanical desk calculator. The only other option was to use a computer. The least-expensive computer system capable of such math operations at the time cost roughly $30,000 and could only serve one user at a time. With the same money, an organization could buy a LOCI-1 calculator for each member of a team of twelve engineers!

The LOCI-1, was really just the starting point for what Wang Laboratories was capable of doing with their electronic calculators. The calculator engineering team already had more ideas for enhancements to the LOCI, which, in a relatively short-time, resulted in the introduction of the even more powerful LOCI-2, in January of 1965, at a base price of $2,750.

Wang Logo and Model Identification Tag

The LOCI-2 provided two more significant digits of accuracy for the logarithmic functions (ten significant digits), added four magnetic-core-based memory registers (which retained their content while the power was off), and, perhaps most importantly, added the ability for the calculator to be programmed by punched cards, as well as an added counter register that could be used to control loop iteration. The programming capabilities were substantial, with conditional tests and branches, along with a subroutine capability, and Input/Output functions which would allow the calculator to communicate with external peripherals. The I/O capability of the LOCI-2 drastically extended the abilities of the calculator, as it could now connect to all kinds of external devices through a simple I/O bus. The LOCI-2 used the same basic cabinet of the LOCI-1, but the keyboard was significantly more complex, with additional keyboard keys for control of the programming and memory functions, as well as indicators for showing the content of the program counter, decrement counter, and instruction register, and switches for manually entering a program code.