Processor chip's contents
Unit Function
Scanning When a calculator is powered on, it scans the keypad waiting to pick
(Polling) unit up an electrical signal when a key is pressed.
Encoder unit Converts the numbers and functions into binary code.
They are number stores where numbers are stored temporarily
X register and Y
while doing calculations. All numbers go into the X register first; the
register
number in the X register is shown on the display.
The function for the calculation is stored here until the calculator
Flag register
needs it.
The instructions for in-built functions (arithmetic operations, square
Permanent mem roots, percentages, trigonometry, etc.) are stored here
ory (ROM) in binary form. These instructions are programs, stored
permanently, and cannot be erased.
User memory The store where numbers can be stored by the user. User memory
(RAM) contents can be changed or erased by the user.
Arithmetic logic The ALU executes all arithmetic and logic instructions, and provides
unit (ALU) the results in binary coded form.
Binary Converts binary code into decimal numbers which can be displayed
decoder unit on the display unit.
Clock rate of a processor chip refers to the frequency at which the central processing
unit (CPU) is running. It is used as an indicator of the processor's speed, and is
measured in clock cycles per second or the SI unit hertz (Hz). For basic calculators, the
speed can vary from a few hundred hertz to the kilohertz range.
An office calculating machine with a paper printer
Example
A basic explanation as to how calculations are performed in a simple four-function
calculator:
To perform the calculation 25 + 9, one presses keys in the following sequence on most
calculators: 2 5 + 9 = .
When 2 5 is entered, it is picked up by the scanning unit;
the number 25 is encoded and sent to the X register;
Next, when the + key is pressed, the "addition" instruction
is also encoded and sent to the flag or the status register;
The second number 9 is encoded and sent to the X register.
This "pushes" (shifts) the first number out into the Y register;
When the = key is pressed, a "message" (signal) from the flag
or status register tells the permanent or non-volatile
memory that the operation to be done is "addition";
The numbers in the X and Y registers are then loaded into
the ALU and the calculation is carried out following
instructions from the permanent or non-volatile memory;
The answer, 34 is sent (shifted) back to the X register. From
there, it is converted by the binary decoder unit into a decimal
number (usually binary-coded decimal), and then shown on the
display panel.
Other functions are usually performed using repeated additions or subtractions.
Numeric representation
Main article: Binary-coded decimal
Most pocket calculators do all their calculations in BCD rather than a floating-point
representation. BCD is common in electronic systems where a numeric value is to be
displayed, especially in systems consisting solely of digital logic, and not containing a
microprocessor. By employing BCD, the manipulation of numerical data for display can
be greatly simplified by treating each digit as a separate single sub-circuit. This matches
much more closely the physical reality of display hardware—a designer might choose to
use a series of separate identical seven-segment displays to build a metering circuit, for
example. If the numeric quantity were stored and manipulated as pure binary, interfacing
to such a display would require complex circuitry. Therefore, in cases where the
calculations are relatively simple, working throughout with BCD can lead to a simpler
overall system than converting to and from binary.
The same argument applies when hardware of this type uses an embedded
microcontroller or other small processor. Often, smaller code results when representing
numbers internally in BCD format, since a conversion from or to binary representation
can be expensive on such limited processors. For these applications, some small
processors feature BCD arithmetic modes, which assist when writing routines that
manipulate BCD quantities.[3][4]
Where calculators have added functions (such as square root, or trigonometric
functions), software algorithms are required to produce high precision results. Sometimes
significant design effort is needed to fit all the desired functions in the limited memory
space available in the calculator chip, with acceptable calculation time.[5]
Calculators compared to computers
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The fundamental difference between a calculator and computer is that a computer can
be programmed in a way that allows the program to take different branches according to
intermediate results, while calculators are pre-designed with specific functions (such
as addition, multiplication, and logarithms) built in. The distinction is not clear-cut: some
devices classed as programmable calculators have programming functions, sometimes
with support for programming languages (such as RPL or TI-BASIC).
For instance, instead of a hardware multiplier, a calculator might implement floating
point mathematics with code in read-only memory (ROM), and compute trigonometric
functions with the CORDIC algorithm because CORDIC does not require much
multiplication. Bit serial logic designs are more common in calculators whereas bit
parallel designs dominate general-purpose computers, because a bit serial design
minimizes chip complexity, but takes many more clock cycles. This distinction blurs with
high-end calculators, which use processor chips associated with computer and
embedded systems design, more so the Z80, MC68000, and ARM architectures, and
some custom designs specialized for the calculator market.
History
Precursors to the electronic calculator
Main article: Mechanical calculator
See also: Human computer
The first known tools used to aid arithmetic calculations were: bones (used to tally items),
pebbles, and counting boards, and the abacus, known to have been used
by Sumerians and Egyptians before 2000 BC.[6] Except for the Antikythera
mechanism (an "out of the time" astronomical device), development of computing tools
arrived near the start of the 17th century: the geometric-military
compass (by Galileo), logarithms and Napier bones (by Napier), and the slide
rule (by Edmund Gunter).
17th century mechanical calculators
In 1642, the Renaissance saw the invention of the mechanical calculator (by Wilhelm
Schickard[7] and several decades later Blaise Pascal[8]), a device that was at times
somewhat over-promoted as being able to perform all four arithmetic operations with
minimal human intervention.[9] Pascal's calculator could add and subtract two numbers
directly and thus, if the tedium could be borne, multiply and divide by repetition.
Schickard's machine, constructed several decades earlier, used a clever set of
mechanised multiplication tables to ease the process of multiplication and division with
the adding machine as a means of completing this operation. (Because they were
different inventions with different aims a debate about whether Pascal or Schickard
should be credited as the "inventor" of the adding machine (or calculating machine) is
probably pointless.[10]) Schickard and Pascal were followed by Gottfried Leibniz who
spent forty years designing a four-operation mechanical calculator, the stepped reckoner,
inventing in the process his leibniz wheel, but who couldn't design a fully operational
machine.[11] There were also five unsuccessful attempts to design a calculating clock in
the 17th century.[12]
The Grant mechanical calculating machine, 1877
The 18th century saw the arrival of some notable improvements, first by Poleni with the
first fully functional calculating clock and four-operation machine, but these machines
were almost always one of the kind. Luigi Torchi invented the first direct multiplication
machine in 1834: this was also the second key-driven machine in the world, following that
of James White (1822).[13] It was not until the 19th century and the Industrial
Revolution that real developments began to occur. Although machines capable of
performing all four arithmetic functions existed prior to the 19th century, the refinement of
manufacturing and fabrication processes during the eve of the industrial revolution made
large scale production of more compact and modern units possible. The Arithmometer,
invented in 1820 as a four-operation mechanical calculator, was released to production in
1851 as an adding machine and became the first commercially successful unit; forty
years later, by 1890, about 2,500 arithmometers had been sold[14] plus a few hundreds
more from two arithmometer clone makers (Burkhardt, Germany, 1878 and Layton, UK,
1883) and Felt and Tarrant, the only other competitor in true commercial production, had
sold 100 comptometers.[15]
Patent image of the Clarke graph-based calculator, 1921
It wasn't until 1902 that the familiar push-button user interface was developed, with the
introduction of the Dalton Adding Machine, developed by James L. Dalton in the United
States.
In 1921, Edith Clarke invented the "Clarke calculator", a simple graph-based calculator
for solving line equations involving hyperbolic functions. This allowed electrical engineers
to simplify calculations for inductance and capacitance in power transmission lines.[16]
The Curta calculator was developed in 1948 and, although costly, became popular for its
portability. This purely mechanical hand-held device could do addition, subtraction,
multiplication and division. By the early 1970s electronic pocket calculators ended
manufacture of mechanical calculators, although the Curta remains a popular collectable
item.
Development of electronic calculators
The first mainframe computers, using firstly vacuum tubes and later transistors in the
logic circuits, appeared in the 1940s and 1950s. This technology was to provide a
stepping stone to the development of electronic calculators.
The Casio Computer Company, in Japan, released the Model 14-A calculator in 1957,
which was the world's first all-electric (relatively) compact calculator. It did not use
electronic logic but was based on relay technology, and was built into a desk.
Early calculator light-emitting diode (LED) display from the 1970s (USSR)
In October 1961, the world's first all-electronic desktop calculator, the British Bell
Punch/Sumlock Comptometer ANITA (A New Inspiration To Arithmetic/Accounting) was
announced.[17][18] This machine used vacuum tubes, cold-cathode tubes
and Dekatrons in its circuits, with 12 cold-cathode "Nixie" tubes for its display. Two
models were displayed, the Mk VII for continental Europe and the Mk VIII for Britain and
the rest of the world, both for delivery from early 1962. The Mk VII was a slightly earlier
design with a more complicated mode of multiplication, and was soon dropped in favour
of the simpler Mark VIII. The ANITA had a full keyboard, similar to
mechanical comptometers of the time, a feature that was unique to it and the
later Sharp CS-10A among electronic calculators. The ANITA weighed roughly 33
pounds (15 kg) due to its large tube system.[19] Bell Punch had been producing key-
driven mechanical calculators of the comptometer type under the names "Plus" and
"Sumlock", and had realised in the mid-1950s that the future of calculators lay in
electronics. They employed the young graduate Norbert Kitz, who had worked on the
early British Pilot ACE computer project, to lead the development. The ANITA sold well
since it was the only electronic desktop calculator available, and was silent and quick.
The tube technology of the ANITA was superseded in June 1963 by the U.S.
manufactured Friden EC-130, which had an all-transistor design, a stack of four 13-digit
numbers displayed on a 5-inch (13 cm) cathode ray tube (CRT), and introduced Reverse
Polish Notation (RPN) to the calculator market for a price of $2200, which was about
three times the cost of an electromechanical calculator of the time. Like Bell Punch,
Friden was a manufacturer of mechanical calculators that had decided that the future lay
in electronics. In 1964 more all-transistor electronic calculators were
introduced: Sharp introduced the CS-10A, which weighed 25 kilograms (55 lb) and cost
500,000 yen ($4586.74), and Industria Macchine Elettroniche of Italy introduced the IME
84, to which several extra keyboard and display units could be connected so that several
people could make use of it (but apparently not at the same time).
The Bulgarian ELKA 22 from 1967
There followed a series of electronic calculator models from these and other
manufacturers, including Canon, Mathatronics, Olivetti, SCM (Smith-Corona-
Marchant), Sony, Toshiba, and Wang. The early calculators used hundreds
of germanium transistors, which were cheaper than silicon transistors, on multiple circuit
boards. Display types used were CRT, cold-cathode Nixie tubes, and filament lamps.
Memory technology was usually based on the delay line memory or the magnetic core
memory, though the Toshiba "Toscal" BC-1411 appears to have used an early form
of dynamic RAM built from discrete components. Already there was a desire for smaller
and less power-hungry machines.
Bulgaria's ELKA 6521,[20][21] introduced in 1965, was developed by the Central Institute
for Calculation Technologies and built at the Elektronika factory in Sofia. The name
derives from ELektronen KAlkulator, and it weighed around 8 kg (18 lb). It is the first
calculator in the world which includes the square root function. Later that same year were
released the ELKA 22 (with a luminescent display)[20][22][23] and the ELKA 25, with an in-
built printer. Several other models were developed until the first pocket model, the ELKA
101, was released in 1974. The writing on it was in Roman script, and it was exported to
western countries.[20][24][25]
Programmable calculators
Main article: Programmable calculator
The Italian Programma 101, an early commercial programmable calculator produced by Olivetti in
1964
The first desktop programmable calculators were produced in the mid-1960s. They
included the Mathatronics Mathatron (1964) and the Olivetti Programma 101 (late 1965)
which were solid-state, desktop, printing, floating point, algebraic entry, programmable,
stored-program electronic calculators.[26][27] Both could be programmed by the end user
and print out their results. The Programma 101 saw much wider distribution and had the
added feature of offline storage of programs via magnetic cards.[27]
Another early programmable desktop calculator (and maybe the first Japanese one) was
the Casio (AL-1000) produced in 1967. It featured a nixie tubes display and had
transistor electronics and ferrite core memory. [28]
The Monroe Epic programmable calculator came on the market in 1967. A large, printing,
desk-top unit, with an attached floor-standing logic tower, it could be programmed to
perform many computer-like functions. However, the only branch instruction was an
implied unconditional branch (GOTO) at the end of the operation stack, returning the
program to its starting instruction. Thus, it was not possible to include any conditional
branch (IF-THEN-ELSE) logic. During this era, the absence of the conditional branch was
sometimes used to distinguish a programmable calculator from a computer.
The first Soviet programmable desktop calculator ISKRA 123, powered by the power
grid, was released at the start of the 1970s.
