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Wang LOCI-2

Updated 5/16/2020

The Wang LOCI-2 (with LOCI pronounced "low-sigh") calculator is of definite significance, partly due to its pretty amazing capabilities for the 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. The LOCI-1 was introduced in September of 1964, with the LOCI-2 introduced shortly thereafter, in January of 1965. With only a few months of time on the market, the LOCI-1, was quickly rendered somewhat irrelevant by the introduction of the LOCI-2, giving the LOCI-1 a short market lifetime, despite it being somewhat less-expensive than the LOCI-2. Though less-expensive, savvy calculator buyers quickly realized that the additional capabilities (most notably, punched-card programmability, the addition of four non-volatile (magnetic core memory-based) store/recall memory registers, and improved accuracy, along with external device interfacing capabilities on the later versions of the LOCI-2) of the LOCI-2 made it a much better value, and thus many prospective buyers overlooked the LOCI-1 in favor of purchasing a LOCI-2. In July of '65, Wang announced the LOCI-2A model, which added three more banks of four core-memory-based memory registers to the calculator. The LOCI-2A thus had the capacity of 16 memory registers. Each memory register could hold a single number inlcuding 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 programs, as well as programming in general, much easier.

The museum currently has two Wang LOCI-2 Systems; 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 an output interface to allow connection of an external numeric printer).

The thing that made Wang Labs' LOCI calculators so ground-breaking was that they could perform advanced math operations, with a single keypress 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 mere milliseconds. The magic that the LOCI brought to the table was the unique abililty to perform 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 abililty 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 programmabililty and memory register capabililties of the LOCI-2 models, made the machines big winners in the high-end electronic calculator marketplace. The machines, although rather expensive, began selling lot hotcakes into engineering, laboratory, research, and educational 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 late in 1964 (Note the italicized "announced" - Wang Labs had a habit of announcing calulators 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. Part of the reason behind this is that the 300-series ended up being such a tremendous success for Wang that Dr. Wang didn't want its success diluted by "competition" from the LOCI, even though the LOCI machinies were technically outdated products. Changing the focus of marketing for the LOCI to classify the machines as computers allowed the LOCI machines to continue to sell within the computer market segment, while freeing up opportunities for the new 300-Series calculators in areas where the LOCI wasn't so applicable. This change of marketing tactics led the LOCI-2 to be targeted toward environments where programmable control was needed. In fact, Dr. Wang assigned one of his key engineers, Frank Trantanella, as VP of Systems Development, a group chartered with designing custom systems that used the LOCI-2 as the computing core in diverse applications such as steel mill controls and 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.

Wang Logo and Model Identification Tag

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, which is a circuit capable of storing as many binary bits as there are elements in the shift register, and the bits can be shifted left and right by pulses, and the register could also be loaded with an arbitrary binary pattern in parallel. 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. 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 string on thin wires arranged in an X-Y grid. Through applying appropraite current pulses sthrough 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. The problem with this was that the act of sensing the state of a core required that the core change its state, effectively "forgetting" the previous state. Dr. Wang's solution to this problem was to simply re-write the state of the core that was sensed back to what was just read out of it. This concept became the basis for what became magnetic core memory, a technology that completely 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, mercury or wire-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 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 Post-It® note. 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 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 logic function, for example, four two-input AND gates, or two JK-type flip flops. The 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 a connection to common power-suppy 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 patent was applied for and granted to Dr. Wang for his developments in magnetic core logic and storage principles.

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 out 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.

Enter Chicago-based Warner Swasey. Warner Swasey was a big player in the business of manufacturing machining equipment such as lathes and milling machines for machining raw metal into high-precision parts. Warner Swasey wanted to leverage the electronics expertise of Wang Labs to make control units that would automate the operation of their machining equipment. Prior to the development of Numerical Control (NC) machining equipment, a skilled machinist had to manually operate the metalworking machines, which was expensive, and introduced human error into the machining process. Numerical Control systems eliminated most all of the human operation of the machine, substituting high-resolution servo-motors with precise digital electronic controls in place of the human operator. All the operator had to do was load metal stock into the machine, start the controller's cycle, watch over the machine while it ran, and remove the finished part when the cycle was completed. Warner Swasey management felt that Wang's logic module technology was particularly well-suited to develop a controller for their machining equipment, so a proposal was put together whereby Warner Swasey provided a chunk of capital to Wang in return for a modest share in ownership of the company. There wasn't much development necessary for Wang to put together a prototype machine controller that read a program from a punched paper tape to direct the operation of a Warner Swasey Lathe. Warner Swasey was given all of the information on the design and construction of the controller, and they took off and 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 won double with the deal; they had on-going revenue from the sale of a lot of logic modules and chassis to Warner Swasey, and also got a nice chunk of cash from them. 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 Warney 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 (long 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 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 agreement 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 ramifications for the company. 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 developing an electronic calculator. 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 C/VIII 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 introduced a calculator (the Friden 132) that could calculate square roots automatically. A few other manufacturers had introduced more 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.

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

Another advanced electronic calculator available during this time was the Wyle Laboratories WS-01/WS-02 calculators. The WS-01 used a magnetic disc for its main memory, with the WS-02 replacing the problematic rotating memory with a magnetostrictive delay line. Both machines were otherwise functionally identical. The machine provided three memory registers and could perform automatic square root. Optionally, it could be programmed by a unique punched card transport that would read punched cards taped together either forward or backward to allow branching and looping operations (with cards taped into a loop). While relatively fast, the programming functions were quite slow, especially when iterative operations were required. A logarithm function could be programmed this way, and would take a number of seconds to generate the natural logarithm of a given number.

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 core 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, as compared to the LOCI-2's same calculation occurring in milliseconds. Unfortunately, the pre-programmed functions could not not be incorporated into a user-written program.`

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 constants from the number to be processed. operations, such as trigonometric functions or logarithms, mainstays in engineering and scientific applications, still had to be done with tables, or relegated to large and expensive digital computer systems. Dr. Wang put his mind to the challenge, and came up with a design for a relatively simple set of digital circuits that would generate the natural logarithm of an arbitrary number quickly and accurately. This circuit would form the foundation of the machine that would catapult Wang Labs out of the doldrums created by the loss of the Compugraphi Linasec business, making Wang 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 concept of the the future powerhouse that Wang Laboratories would become in the calculator marketplace.

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, set the stage for Wang's first production calculator, the LOCI-1, which had a sales price of $2,750. The LOCI-1 could add, subtract, multiply, and divide, as well as generate natural logarithms (with around eight digits of accuracy) and perform anti-logarithm with a single keystroke. The LOCI-1 also performed one-key squaring and square root, along with the unusual inclusion of single-key calculation of the reciprocal of the square of a number, or the reciprocal of the square root of a number. Being able to perform these functions with a single keypress, and have a result in milliseconds was truly mind-blowing for the time. The only way to perform these kinds of calculations prior to the existence of the LOCI-1 was either to work out the results by-hand, using logarithm tables or slide-rules(which had limited accuracy) and a mechanical desk calculator, or to resort to the use of an expensive computer system. The LOCI-1, though, was essentially just a starting point for what Wang Laboratories was capable of doing with their electronic calculators. The engineering team already had more ideas for enhancements for the LOCI, which, in a relatively short-time, resulted in the introduction of the even more aamazing LOCI-2.

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.

Documentation from Wang Laboratories indicates that the LOCI-1 was "no longer in production" in 1965, which would have meant that number of LOCI-1 calculators produced and sold was quite small. If you have or know the whereabouts of a Wang LOCI-1 calculator, please contact the Old Calculator Museum by clicking the EMail button at the top of this page.

While the LOCI-1 had a short market lifetime, the LOCI-2 had a feature set that was extremely marketable at the time, especially to engineering and scientific users. The ability of a low-cost, desktop-sized calculator to be able to perform functions that heretofore were relegated to computing systems costing orders of magnitude more. On top of the huge cost-effectiveness of the systems, they were quite simple to program, and the fact that they operated in human-friendly decimal, instead the computer- friendly binary code used in computers, made them much easier to use for general scientific and engineering calculating applications. Wang Labs toured the LOCI-2 around to various electronics trade shows and exhibitions, and the machine was an instant hit with scientists, engineers, and mathematicians because of its ability to perform higher level math functions with great speed, along with its ability to be programmed via punched cards. The booths at trade shows where the LOCI-2 was shown were packed with people who wanted to find out more about the machines, with many who learned about the machines capabilties placing orders. It is known that in 1965, LOCI-2 serial number 0003 was sold to the US Navy, for use in data reduction of aircraft flight test data. The LOCI-2 reduced the time for a typical data reduction calculation from 15 minutes performed on an early electronic four-function desk calculator, to less than one second! Such was the power and speed of the LOCI-2. (Sincere thanks to John McHale, USN Naval Air Systems Command, Retired, for information on LOCI-2 #0003).

The secret to the advanced functionality of the LOCI calculators was Dr. Wang's logarithm calculating circuit. With logarithms, it is very simple to perform complex math functions by simply performing addition and subtraction of logarithms. Slide rules, the inseparable companions strapped to the belts of engineers and scientists before electronic calculators existed, used logarithmic scales in order to perform multiplication and division along with other higher-level functions. With conventional logic circuits of the day, multiplication and division required fairly complex circuitry. With Dr. Wang's logarithm circuit, multiplication and division became simple addition and subtraction of logarithms. Wang's calculator was really no more than an electronic adding machine with addition of the logic that Dr. Wang had invented that allowed logarithms and anti-logarithms to be calculated quickly and accurately. The real kicker was that the logic of the digital logarithm generation system was not terribly complex, making the logarithmic capability reasonably inexpensive to implement even with discrete transistorized circuitry. More accurately stated, the LOCI-2 was a much higer accuracy electronic implementation of an old-fashioned slide rule! Along with the advanced math capabilities that the logarithmic functionality brought to the machine the ability of the LOCI-2 to be programmed using a punched-card reader allowed the machine to automatically carry out highly complex mathematical functions which made the LOCI-2 closer to a true computer than a calculator. All of this occurred at a time when the rest of the electronic calculator marketplace was offering basic four-function calculators, with perhaps a few memory registers, and little, if anything in the way of programmability. During the lifetime of the LOCI-2, the calculator became the computing core of a number of complex systems. Because of the extensible nature of the LOCI-2's I/O design, it was possible to interface the LOCI-2 to a wide range of peripherals. This flexibility allowed the calculator to end up being used as the brains for quite a number of custom control systems, such as the space suit environmental system testing device (pictured above). The popularity of Wang's custom systems led to some generalized data acquisition and control systems. An example of a system using the LOCI-2 as the "CPU" is the Wang Model 2315 "On Line Computing System", a general-purpose data acquisition and data processing system that could serve as the basis for a complex process control environment, at a much lower cost than any other available technology of the time. The ability of the LOCI-2 to be used in such wide-ranging applications is a testimony to the brilliance of those involved in the design of the machine.

LOCI-2 Keyboard Layout

By the very nature of its advanced capabilities, the LOCI-2 is a pretty complex machine, with over 1200 transistors. Some early transistorized computers had fewer transistors than the LOCI-2. However, the transistors used were high-volume, low-cost devices that had been tried and true in the digital electronics realm, so, despite the large number of transistors, the cost of the machine was still quite reasonable. The amazing capabilties of the machine made it a bit different from traditional electronic calculators of the time from an operator point of view, and took some serious getting used to for folks that either had used mechanical calculators, or other electronic calclators, or for those that had never used a calculating instrument before. The machine has great capability, but that capability came at the cost of intuitive operation. It was this complexity that led Dr. Wang to have his designers investigate ways to make the machine easier to use, and a result of that research, the next generation of Wang electronic calculators debuted not that long after the LOCI-2. The Wang 300-series machines (an example in the museum is the Wang 360SE) very quickly took over the majority of Wang's calculator sales, and within a year of introduction became Wang Laboratories' primary source of revenue. The LOCI-2 was much more suited to engineering or scientific users and was overkill for general use by less technically-mided users. After the 300-series calculators hit the market, the marketing for the LOCI-2 was changed to target complex data acquisition, data analysis, and process control applications, putting the high-speed math operations, programmability, and I/O capabilies of the machine to these tasks.

The thought that comes to mind when one sees the LOCI-2 for the first time is, "What are all those keys for, and how do you do anything with it?" Some of the keys have cryptic nomenclature, such as the [□] key. With a little thought, it becomes clear that the function of this key is to perform a squaring (get it? the "square" key) operation, e.g., x2. It seems like it would have been more intuitive to simply put x2 on the keycap, but for whatever reason, this more cryptic representation was chosen.

LOCI-2 with Cabinet Removed

The insides of the LOCI-2 are quite amazing. The electronic brains of the machine are made up of a total of nine rather large circuit boards. The circuit boards are made of high-quality fiberglass that have traces on both sides of the board, with plated-thru holes for connection of traces between each side of the board. For the time, plated-thru holes (also known as "vias") in circuit boards were quite advanced. Many competitors, especially the Japanese manufacturers, had to solder small pieces of wire through via holes to conduct signals from one side of the board to another, as their circuit board manufacturing processes simply could not create reliable plated-thru holes. The edge-card fingers of the LOCI-2 circuit boards are simple tin-plated copper, and prone to corrosion, which can make the machine malfunction if not kept corrosion-free. Why Wang Labs didn't use gold-plated edge connector finges and sockets is a real mystery, as use of gold plating on the circuit board edge card fingers would have eliminated a lot of problems with corrosion caused by ambient moisture in the air. It was likely due to cost, as it was rather expensive to gold-plate the copper of the edge connector fingers as opposed to tin plating.

Some of the circuit boards in the museum's machines have dates as included as part of the circuit board artwork. Most of the dates, which I assume are used to keep track of circuit board revisions, are from the late 1965 (September) through early 1966 (April) timeframe. Each of the circuit boards contains a great many transistors, and literally hundreds of diodes, along with myriad resistors and capacitors. Each board has an aluminum stiffener pop-riveted to the top edge of the board to add mechanical stability to the board. The circuit boards plug into a hand-wired backplane that provides interconnections between the boards as well as connections to the keyboard assembly. The cards are retained by aluminum panels on each end that have plastic card guides pressed into them to keep the cards in alignment. Of the nine circuit boards in the machine, only three have obvious functions. All of the rest of the boards seem to be a fairly random scattering of diode-resistor and transistor logic gate circuits and flip flops. Dr. Wang was quite protective of his designs, and rumor has it that efforts were purposely made to make it difficult to reverse-engineer the design of the machine. Some of the information included below on the function of the individual circuit boards was determined by observing the calculator with logic analysis instrumentation while it was in operation.

1501A Instruction Register and Decoder (Left) & 1401A Display (Right) Boards
Click on Circuit Board Images for Larger View and Description of Logic on the Board

The front-most board in the machine contains the instruction register (six flip flops) and a large array of diodes used to decode the instruction code. The board is about half as tall as the other boards in the machine, mostly to allow the Nixie tubes on the board behind it to be seen through the display panel. This board breaks the six-bit instruction code (coming either from the punched card programmer or from the keyboard) into various signals that govern the sequencing of the calculator to perform the operation specified by the operation code in the instruction register.

Close up view of National Electronics top-view Nixie tubes used in LOCI-2 (Note discrete neon lamps used for decimal point indication)

The 2nd board is the display board. This board contains all of the decoding logic to drive the unusual top-view Nixie tubes. The Nixie tubes are similar to the original design Burroughs Nixie tube, where the digits are viewed from the top of the glass envelope of the tube, rather than through the side of the envelope like most other Nixie tube implementations used in calculators. The Nixie tubes plug into sockets, making for easy field service replacement should a failure occur. Each Nixie tube has its own set of ten driver transistors and a diode-based decoding array to turn a four-bit binary coded decimal code into the one-of-ten signal to drive the tube. The left-most tube in the display is a special Nixie that has a "+" and "-" sign in it (along with an odd upside-down 8, which isn't used in this application), used for indication of the sign of the number in the display.

The 1402A W (Working) Register & Adder (Left) Board & 1403A L (Logarithm) Register and Log Adder (Right) Board
Click on Circuit Board Images for Larger View and Description of Logic on the Board

The 1404A Timing & Log Generation Sequencing (Left) & 1405A Miscellaneous Function(Right) Boards
Click on Circuit Board Images for Larger View and Description of Logic on the Board

1406A A (Accumulator) Register(Left) & The 1408A DC and PC Programming Registers(Right) Boards

The remainder of the boards, except for the last board, all make up the logic that makes the machine run. Three of the boards contain mostly flip flops arranged in regular arrays, making up the three primary operating registers (W, A, and L) of the calculator. Along with all of the flip flops, there are countless DTL (Diode-Transistor Logic) gates that provide the combinatorial logic. The W register is the "Working" register, which really means the display register. Whatever is in the W register is shown on the display. The A register is an accumulator register, where addition and subtraction operations are performed. Addition and subtraction operations add or subtract the content of the W register to/from the A register. The L register is the special logarithm register. It is also an accumulator-style register, meaning that it can be added to or subtracted from, but there is no direct entry to the L register. The Logarithmic functions, as well as multiplication and division operations, store into, and add or subtract logarithms generated by the logarithm logic to/from the L register. The L register contains 12 digits, with the first two digits being in front of the implied decimal point, and the remaining ten digits behind the decimal. With this representation, the L register can conceivably hold numbers ranging from e-99.9999999999 (about 3.72008x10-44) to e99.9999999999 (approximately 2.68811x1043, which is a large range of numbers. However, since the working register only contains 10 digits, the practical limits of the L register range from approximately -23.0258509298 (roughly .0000000001) to 23.0258509298 (about 9,999,999,999).

The Wang LOCI "Column Printer" (Option D)
Image Courtesy Sarah Hafner

The backplane of the LOCI-2 contains ten slots. The ninth slot (slots are numbered 1 through 10, front to rear) is for an optional Input/Ouput expansion. Some models of the LOCI-2 have this slot unpopulated, with empty cutouts for the edge connectors in the chassis, and block-off plates on the back panel where the I/O connectors would be. On LOCI-2's with the optional I/O expansion, slot nine is populated with edge connectors in the backplane, additional wiring connecting the ninth circuit board into the other calculator boards, and two connectors on the back panel of the calculator, labeled "INPUT" and "OUTPUT". A number of different Input/Output interfaces were available for the LOCI-2, including two different interfaces which would allow the connection of a Teletype Model 33-ASR ASCII electromechanical data terminal (Options C, E, and H), as well as the "LOCI Printer" (see above, Option D) that provides a 12-column printer to record results of calculations on adding-machine tape. The column printer is housed in its own large cabinet with a pull-out drawer containing the printer module, with the rest of the cabinet containing power supply, interface logic circuitry, and the driver circuitry for the printer.

The 1410A Core Memory Control Board

The rear-most board in the LOCI-2A model controls the core memory used in the machine for memory register storage. The core plane is mounted on the rear of this circuit board, and connects to the circuit board with two small edge connectors.

LOCI-2's Core Memory Array

The core array has 16 words of 12 bits each, and is four planes deep. This makes for a total storage of 16 12-digit BCD numbers. According to the LOCI-2 Reference Manual, LOCI-2 was available with two (flip-flop-based) memory registers, and the LOCI-2A replaced these two flip-flip memory registers with 16 magnetic core-based memory registers. The machines in the museum are both model LOCI-2A machines, which have 16 memory registers, arranged in four banks of four registers. Each memory register is capable of storing a 10 digit number, the decimal point location, and sign (using a total of 48 bits).

The Backplane and some Power Supply Circuitry

The base of the machine contains the backplane and power supply. The backplane is a maze of individual wires that connect the circuit boards together. Each wire has a clip on the end that tightly grabs the terminal of the edge connector pin that it is connected to. This connection technology is rather unique -- usually wire wrap (a technology where a number of turns of bare wire is tightly wrapped around the terminal) was used for such connections. It is a testimony to this technology that it is robust enough to still provide solid connections over 40 years later.

View from the rear, showing Power Supply and Core Stack

The power supply of the LOCI-2 is a very simple linear supply. A good-sized transformer steps down the line voltage to a number of AC working voltages, which are rectified and filtered in the usual ways. There is no regulation for the supply voltages, instead, a high-wattage variable resistor is used to set the proper supply voltage of the 5.5V supply with the power supply under load. Power supply voltages are -12V and +5.5V DC.

The LOCI Card Reader (1st Design)

The LOCI Card Reader (2nd Design) and Punched Card

The LOCI-2 is a programmable calculator. Programs are 'stored' on a punched card. The LOCI-2 has no memory for storing programs internally, the program steps are simply read off of the card, one step at a time, and executed in order. The external (optional) card reader is plugged into a port labelled "CARD READER" on the back panel of the LOCI-2. Two versions of card reader were available for LOCI, with an early version (available when the LOCI-2 was introduced), and a later design unit that improved the reliability of card reading, becoming available about 8 months after the LOCI-2 was introduced. Both function the same. The card reader uses punched cards that were manufactured for Wang by IBM (IBM Part #D56709), and consist of 40 columns (half the number of columns of a standard Hollerith punched card) of 12 rows each. The cards have pre-scored punch-out holes that can easily be punched out by using a pencil point. An accessory called a "Port-O-Punch" was available from Wang (though the Port-O-Punch was made by IBM, and Wang Labs purchased the devices from IBM under an OEM contract) that served as a fixture to allow for easier punching of program cards, and collection of the punches (also known as "chad"). Each card holds 80 steps of program code, with each step being a six bit function code. The bottom six rows of the card contain steps 00 through 39 (left to right), and the top six rows contain steps 40 through 79. Once a card was prepared with a program, the card reader was opened, the card placed inside, and the reader closed. The reader reads the cards by using a 40x12 'bed of nails' array. A set of contacts is pressed against each area on the card where a hole can be, and if a hole is there, an electrical connection is made.

A Closer View of the "Bed of Nails" in the 2nd Design Card Reader

The card reader has circuitry inside it to allow the programmer in the calculator to select a given program step based on the content of the Program Counter, and relay the six bit code punched into the card to the calculator for execution.

LOCI-2 2nd Design Punched Card Reader Circuitry

The programming functions of the calculator is controlled by keys and switches located at the right end of the keyboard panel. The main key for controlling the programming functions of the LOCI-2 is a key labeled [RUN]. This key initiates action of the programmer as defined by the state of the mode switch. A single three-position toggle switch controls the mode of the programmer, with selections for "STEP", "AUTO" and "MANL" (manual). In step mode, the calculator executes a single instruction each time the [RUN] key is pressed. This is useful for stepping through programs to verify that they were punched properly into the card, as well as providing a means for debugging programs. When the mode switch is in "AUTO" mode, the calculator beings full-speed execution of the program at the current location of the program counter upon pressing the [RUN] key. When the mode switch is in the "MANL" position, a bank of six toggle switches is activated that allow a program code to be toggled into the switches, and be executed (without modifying the program counter) with a press of the [RUN] key. Three rows of neon indicators show the status of the programmer registers in binary form.

The top-most row of indicators shows the content of the "DECREMENT COUNTER". The decrement counter is used for program counting and looping functions. A number from 00 through 99 can be loaded into the decrement counter under program control. The decrement counter counts in Binary Coded Decimal. Once the decrement counter is loaded with a number, a program instruction can cause the counter to decrement by one. A program instruction can check the decrement counter for zero content, causing a branch to occur if the decrement counter is zero.

The middle row of indicators, labeled "PROGRAM COUNTER", shows the content of the program counter. The program counter is an eight bit register with somewhat odd counting behavior. The most-significant four bits of the program counter count in binary form, i.e., 0-15, but the least-significant four bits count in BCD form, e.g., 0-9. This means that the program counter has the capacity to count up to 160 steps, though a punched card only has 80 steps. An additional 80 program steps could be gained through addition of a second card reader.

The program counter can be preset to four 'program start' locations by four keys on the calculator keyboard labeled [P0], [P1], [P2], and [P3]. These keys set the program counter to 00, 03, 06, or 09 respectively. If the programmer is in "AUTO" mode, pressing one of the [Px] keys causes the program counter to be set to the appropriate starting step number and program execution to begin at that step. This operation allows the [Px] keys to be used as user-definable function keys in programs.

An "official" Wang LOCI Programming Form

The program counter can also be set programmatically, via an instruction that loads the two upper digits of the display register into the program counter (essentially an unconditional jump). The program counter normally increments one program step at a time as program steps are executed. Branching instructions, however, cause the program counter to be incremented by three steps if the condition the branch is checking is true. Along with the unconditional and conditional branching instructions, the calculator has a subroutine capability. The "Store and Jump" instruction stores the content of the Decrement Counter and Program Counter in an auxiliary set of registers, and a branch taken to the subroutine at the address defined by the upper two digits of the W (display) register. When the subroutine is completed, the "Restore" instruction causes the Program Counter and Decrement Counter to be restored from the auxilliary registers, returning control to the instruction following the subroutine branch.

The bottom row of indicators show the six bit operation code punched into the card at the current location of the program counter, useful for verifying that a card was punched correctly.

The LOCI-2 Instruction Set
00 No Operation 20 0 (Zero) 40 W -> PC 60 P0
01 Clear Error 21 1 41 W -> XPC 61 P1
02 Clear W 22 2 42 W -> DC 62 P2
03 Clear A 23 3 43 DC -> W 63 P3
04 Sq. Root 24 4 44 W -> A 64 Store & Jump
05 1/Sq. root 25 5 45 A -> W 65 Restore
06 Square 26 6 46 W -> L 66 Decrement
07 1/Square 27 7 47 L -> W 67 Test Error
10 Step MSC 30 8 50 A -> S0 70 Test DC=0
11 WRITE 31 9 51 S0 -> A 71 Test A=0
12 X (Mult.) 32 RUN 52 W -> S1 72 Test W=0
13 + 33 Chg. Sign 53 S1 -> W 73 Test W<0
14 ANTILOG 34 Load Input MX 54 W -> S2 74 Test L<0
15 - 35 Load Output MX 55 S2 -> W 75 Car'ge Return
16 Decimal Pt. 36 PRIME 56 W -> S3 76 READ
17 Divide 37 STOP 57 S3 -> W 77 Undefined

All of the 64 possible program operation codes correspond to a given function the calculator can perform. Each key on the keyboard is represented by a specific key code. Along with codes for each of the keys on the keyboard, there are miscellaneous function codes that allow control functions such as the test and skip instructions (for conditionals and branching), for control of the decrement counter, input/output, and stopping the program for user data input.

Front Cover of Very Early Wang LOCI Reference Manual (August, 1965) - Courtesy Frank Trantanella
Front Cover of Later LOCI-2 Reference Manual

The operator's panel layout of the LOCI-2 is probably now used as a study in how not to design for human factors. There are a lot of keys, and they are organized in such a way that it isn't always easy to find what you are looking for, for example, the [0] and [.] keys are located to the left of the numeric keypad..a seemingly odd location compared to the standard layout that we are used to today. The nomenclature on the keys is also somewhat cryptic. Along with these annoyances, the machine is not entirely straightforward to operate, with a myriad of registers, and an unusual entry method for all functions but addition and subtraction. All of these factors combined to make the machine a bit of a challenge to operate (and program), which likely prompted Wang to quickly begin development of a machine with a similar architecture, but that operated in a more straightforward manner, the Wang 300-series calculators.

The architecture of the machine is centered around three main registers, the W (Working) register, the A (Adder) register, and the L (Logarithm) register. All three of these working registers of the calcuator are composed of individual flip flop storage elements. The W register is the data entry register. The Nixie display always shows the content of the W register. The W register is where numbers are entered into the machine, and where results are displayed. The [CLEAR W] key clears the W register, and is mainly used for correcting input errors.

The A register serves as an accumulator, where addition and subtraction operations are performed. The [+] and [-] keys act by adding/subtracting the content of the W register to/from the A register, with the result returned to the A register. Note that the result is placed in the (non-displayed) A register rather than in the W register. In order to view the result of an addition or subtraction, the [A→W] key must be pressed to copy the content of the A register to the W register for display. It appears that Wang realized that this was a bit confusing, and added a toggle switch at the lower-left corner of the keyboard called "AUTO DISP", that, when on, causes an automatic transfer of the A register to the W register on completion of an addition or subtraction operations. A [CLEAR A] key clears the adder register.

Lastly, the "L" register is where Wang's special logarithm circuit comes into play. The L register is also an accumulator, but rather than accumulating normal numbers, the L register accumulates logarithms. The L register has a range of -49.9999999999 to +49.9999999999, the range required to represent the base e logarithm of any number the machine can handle. The multiply, divide, square root, squaring, and reciprocal functions of the calculator all operate through the L register. The L register can be loaded directly from the W register via the [W→L] key, which causes no logarithm to be calculated, but rather just copies the content of the W register into the L register. If the number in the W register is too large, and error condition will result (though, the error checking for the range is not completely robust, and strange results can occur if too large a number is attempted to be directly stored in the L register). The content of the L register can be recalled to the display (W register) by pressing the [L→W] key. Multiplication works by calculating the base e logarithm of the number in the W register, and adding it to the current content of the L register, placing the resulting total in the L register. Division does the same, but rather than adding the logarithm, it subtracts it. Square root is performed by taking the logarithm of the number in the display, halving it, and adding the result to the L register. The [ANTILOG] key provides the translation back to regular numbers from the logarithm, by calculating the anti-logarithm of the number in the L register, and putting the result into the W register for display. So, with this arrangement, let's explore how one would perform a simple multiplication on the LOCI-2. First, the [PRIME] button is pressed to clear the machine. Then, the first number in the multiplication problem would be entered. Then, the [X] key is pressed. This causes the logarithm of the number in the display to be calculated and added to the L register. Then, the second number is entered, followed by the [X] key. This calculates the logarithm of the second number, adding it to the log of the first number already in the L register. At this point, the L register contains the logarithm of the product of the two numbers. To display the result, the [ANTILOG] key is pressed. This causes the antilogarithm of the result in the L register to be calculated, and transferred into the W register. As an example, below is a walk-through of performing 20.5 multiplied by 15:

PRIME +0.000000000 +0.000000000 +00.0000000000
2 +2 00000000 +2.000000000 +00.0000000000
0 +20 0000000 +20.00000000 +00.0000000000
. +20. 0000000 +20.00000000 +00.0000000000
5 +20.5 000000 +20.50000000 +00.0000000000
X +0.000000000 +0.000000000 +03.0204248860
1 +1 00000000 +1.000000000 +03.0204248860
5 +15 0000000 +15.00000000 +03.0204248860
X +0000000000 +0.000000000 +05.7284750870
ANTILOG +307.4999999 +307.4999999 +00.0000000000

There are four other math functions that operate on the L register. These include the [□] key (as mentioned before, performs an x2 operation); a [1/□] key, which squares the argument, then calculates its reciprocal; [√]; and [1/√]. Each of these functions operate on the argument in the W register, and accumulate the result in the L register.

One of the quirks of the logarithmic method of performing math is that the base e logarithm of most numbers is a transcendental number, meaning it can never be represented exactly, no matter how many digits the logarithm is calculated to. As a result, the LOCI-2 could give somewhat unexpected answers to simple problems. As you can see above in the example, performing 20.5 x 15 on the LOCI-2 results in 307.4999999, rather than 307.5 as expected. While technically accurate to one part in ten million, results like this were quite confusing to non-technical users. This perceived problem, along with the generally non-intuitive operation of the machine, made the LOCI-2 difficult to sell into business or non-technical applications. This was pointed out to Dr. Wang by his accountant, who had a fascination for Wang's calculating machines, and as a result, Wang put his engineers to the task of designing a new machine that incorporated a round-off circuit so that our example calculation would result in 307.5, and also improved upon the operational method and keyboard nomenclature to make the machine easier to operate by less technical users. This new machine, which actually turned out to be an entire series of machines, was the Wang 300 calculator -- a product which exponentially multiplied (forgive the pun) the fortunes of Wang Laboratories, and set the course for a period of extremely rapid growth and preeminence in the calculator business.

Along with the three working registers of the machine, the "A" version of the LOCI-2 features a total of 16 non-volatile (meaning that content is retained even when the machine is turned off, even though the reference manual incorrectly states that the memory could be changed by unplugging the machine) store/recall memory registers, which reside in the core memory stack of the machine. In keeping with the unusual architecture of the machine, access to the memory registers is a bit different than most calculators. The memory registers on the LOCI-2 are store/recall registers only -- no arithmetic can directly be performed on the memory registers. There are a total of eight keys that access the memory registers, four for storing numbers into registers, and four for recalling memory registers. At first thought, this may not seem enough keys to handle 16 memory registers. You're right. The memory registers are arranged in four banks of four registers (numbered zero through three) each. A two-bit incrementing register called "MSC" determines which bank of four memory registers is currently accessed by the memory store/recall keys. A key labeled [STEP MSC] increments the MSC register each time it is pressed, and serves as the sole method for the user to select which bank of memory registers is currently being accessed. The [PRIME] key clears the MSC register to "00", and subsequent presses of the [MSC] key advance the memory bank count to "01", "10", and "11", then back to "00". The state of the MSC register is displayed on two neon indicators that peek through the keyboard panel. Of the four registers in each bank, the first register is 'special', in that they transfer between the A register and the memory register (keys [A→S0] and [S0→A]). The remaining three memory store/recall keys transfer between the W register and memory.

The remainder of the keys on the keyboard perform various utility functions. The [PRIME] key is the master reset for the electronics. It clears everything (except the memory registers), and resets the electronics. The [PRIME] key must be pressed before using the machine after it is powered on, or the machine will act VERY strangely, as it appears that there is not an automatic initialization of all of the electronics at power-on time. The [CLEAR ERROR] key is actually a misnomer, in that it really should have been called "TOGGLE ERROR". A neon indicator labeled "ERROR" at the upper left corner of the keyboard panel lights up when error conditions occur, such as asking the machine to calculate the logarithm of 0. The [CLEAR ERROR] key actually toggles the state of this indicator, e.g, if ERROR is on, pressing [CLEAR ERROR] turns it off (as expected), however if ERROR is off, pressing [CLEAR ERROR] turns the ERROR indicator on! The ERROR condition does not lock out the keyboard or have any other effect other than just to serve as a notification that something happened which caused an error condition. A program instruction is provided which can sense the state of the error condition. The [CHANGE SIGN] key toggles the sign of the number in the W register. This key is labeled [+/-] on some LOCI-2 machines.

A couple of keys on the keyboard have different functions depending on options the machine has. If the machine does not have the Input/Output option, two keys labeled [.→] and [.←] can be used to shift the decimal point to the right or the left, and a [&larr] key is used as a backspace key to delete digit entry one digit at a time. On machines that have the I/O option, these three keys are replaced with [READ] and [WRITE], and [C'RG RET] keys, used for receiving input from, sending output to, or returning the carriage to home position on externally connected Input/Output devices.

The LOCI-2 is a fast calculator. Addition and subtraction operations complete virtually instantly. Multiplies and divides are just a shade slower because of the logarithm calculations that must be performed. The 'all nines' divided by one benchmark that I normally use to gauge the speed of a calculator doesn't apply to the LOCI-2 because of the method by which it does division by using logarithms. Because of this method, the complexity of a division problem does not have any bearing on the amount of time that it takes for the calculator to perform the operation. An indicator on the keyboard panel labeled "RESPONSE" lights while the calculator is busy performing an operation. This light never seems to stay lit for more than just a fraction of a second for all math problems thrown at the machine. The programmer also operates very quickly. With the card reader disconnected, the programmer sees nothing but 'NO OPERATION' codes for all program steps. When the [RUN] key is pressed to start the programmer, the "PROGRAM COUNTER" indicators cycle so fast that they all appear on, with just the most significant bit flickering ever so slightly to indicate activity. My guess is that the machine takes less than 1/10 of a second to execute 80 'NO OPERATION' instructions.

Special thanks to Jim Willing for the opportunity to acquire Serial #3086.
Thanks to George Finn for providing helpful insights about the Wang Labs/Compugraphic Linasec.
Special thanks to Sarah Hafner for the opportunity to acquire Serial #3070, a machine originally owned by her father.
Additional thanks to Frank Trantanella, former Wang Laboratories employee, for sharing his experiences with the LOCI calculators and systems.

Text and images Copyright ©1997-2023, Rick Bensene.

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