calculators
INTRODUCTION
Electronic, electromechanical electronic devices that automatize mathematical calculations are called calculators. Calculators perform calculations using the basic Arithmetic functions, including subtraction, multiplication, and division--and many can also perform more complex calculations, including frequente and inverse trigonometric calculations ( see trigonometry). There are few inventions that have had as significant an influence on the daily routine like the handheld, or pocket electronic calculator. These calculators can be used to help save time as well as to decrease chances of making mistakes and can be found in places where individuals are frequently in contact with numbers, such as stores, offices, banks and schools, labs, as well as in private homes.
Early calculatorswere mechanical: they computed using components of machines, such as disks, drums, and gears--that were powered via hand, and later electricity. In the 1950s, many were mechanical calculators were being replaced by electronic calculators with integrated circuits--in some cases like the circuits found in computers--to execute mathematical functions. In fact, the sophisticated electronic calculators nowadays are specially-purpose computers. They contain built-in instructions on how to use certain tasks.
As with other processing systems for data, calculators are of two types--analog and digital. Analog calculators work with various physical quantities that are variable--fluid flow, or voltages for instance--and solve math-related problems by creating physical analogies to the problem. Clocksand slide rules or utility meters are examples from analog calculators. Digital calculators are those that are frequently thought of as calculators. They operate directly with numbers or digits , and operate by listing, counting as well as comparing these digits. Digital calculators include cash registers, adding machines as well as handheld or desktop electronic calculators.
PRINCIPLES OF MECHANICAL CALCULATORS
The basic part of most mechanical calculators includes a set numeral-adding wheels. In a mechanical calculator that is driven by keys (and in the majority of others) these wheels are visible through a row of small windows in the front of the device. Each wheel is adorned with the numbers of 0 through 9 around its edge. Behind each wheel, there is a row of keys that have identical digits. Pressing the key 1 in a column rotates its numeral wheel by one step. pressing the key number 2 turns the wheel for two steps, and it goes on. When the 1 and 2 keys are simultaneously pressed then the wheel will advance one step, and then two moresteps, finally signalling three. Therefore, a column of numbers could be quickly added by simply typing in the numbers in the keyboard, and then reading their totals in the windows. Interlocking mechanisms within the numeral wheels automatically allow for carrying overs. Multiplication is accomplished by repeating addition. Subtraction is accomplished with an indirect method and division is done by repeated subtraction.
PRINCIPLES OF ELECTRONIC CALCULATORS
The electronic calculators are executed by integrated circuits--tiny arrays with thousands or even millions of transistors. These circuits contain permanent instructions for addition, subtraction, multiplication, division as well as (in more advanced calculators) other functions. The numbers that the operator enters are briefly stored in addresses or locations, inside the random-access memory (RAM) that contains enough space to store the numbers that are used and generated at any moment using the calculator. The numbers stored in these locations are processed by circuits that contain the instructions to perform the mathematical operations.
HISTORY
The most ancient calculating aid is the abacus, which has been used for many thousands of years. It consists of movable counters placed on an engraved board or strung across wires. The first version of the slide rule, often regarded as the first calculator to be successful in analog, was invented in 1620 by the English mathematician Edmund Gunter. It was initially employed to multiply or divide numbers by adding or subtracting their logarithms. Later , it was possible utilize slide rules to determine square roots as well as, in some instances, calculate trigonometric operations and logarithms.
MECHANICAL CALCULATORS
The first mechanical digital calculator, which was the predecessor to the modern calculator was an algebraic machine devised by French mathematician Blaise Pascal in 1642 ( see Pascaline). Later in the 17th century Gottfried Wilhelm Leibniz created a higher-tech model of the machine that Pascal had designed. It employed a shaft with progressively longer teeth fixed along the shaft, and a cogwheel with 10 teeth. The edges of the cogwheel could be seen on a dial, and was marked with the numbers 0 to 9. By placing the cogwheel a particular direction on the shaft, and then turning the shaft in a certain direction, two numbers can be added. To multiply two numbers, the shaft was rotated several times. Subtraction was accomplished through turning the shaft in reverse and division was achieved by repeated subtraction.
In 1878 W.T. Odhner created the pinwheel. When a specific number was entered on a machine using this mechanism, the appropriate number of pins were raised by wheels on the main shaft. When the shaft rotated, the pins merged with cogwheels, whose revolutions gave the result to the sum in the same manner as were the cogwheels used in Leibniz's invention. This invention of the pin-wheel was what made it possible to construct cleaner and more easily driven machines.
The first key-driven calculatorlater known as the Comptometer was invented by Dorr Eugene Felt in 1886. Key-driven calculators were operated fast and were often employed in offices. In one kind of key-driven calculator, called a key-set device, the number keys were first pressed or then cocked. Then , a second action--turning the crank or launching with a drive motor, transferred the number set into the keyboard to the wheels for numerals. The principle of key-set was employed to calculate machines that printed their results on paperstape because it was not possible to drive printers directly from the keys.
The first commercially successful Rotary calculator was created by Frank S. Baldwin and Jay R. Monroe in 1912. The first rotary calculators had a rotary motor to transfer numbers that were set on the keyboard into the adding-wheel unit. Since the rotary drive lent itself to high-speed repetitive addition and subtraction that these machines could be able to multiply and divide extremely quickly as well as automatically.
The special-purpose calculators are the ones that include the cash register. It was invented in 1879 , by James Ritty, a storekeeper in order to guarantee the honesty of his clerks. The first bookkeeping machine--an adding-printing device -- was created in 1891, through William S. Burroughs, the bank clerk. Punch-card machinesoriginally employed for controlling the operation of looms, were adapted to information processing during the 1880s, by Herman Hollerith of the United States Bureau of the Census. They read information from cards on which patterns of holes represented both numbers and letters.
ELECTRONIC CALCULATORS
Developments in electronics in the 1940s, 1950s, and 1960s made possible the creation of the computer and electronic calculator. Electronic desktop calculators which were introduced in 1960s, had the same functions as mechanical calculators but had virtually no moving parts. The development of miniature electronic devices that were solid-state brought about an array of electronic calculators which could perform much more functions and more efficient than their mechanical predecessors. Today most mechanical calculators have been replaced by electronic models.
Modern handheld electronic calculators can do not only addition, subtraction, multiplication, and division but also are able to handle square roots percentages, and squaring. This is when the appropriate key is activated. The input data and the final result are displayed on screens using or light emitting diodes (LEDs) or liquid crystal display (LCDs).
Special-purpose calculators have been designed to use in business, engineering as well as in other fields. Some of these are able to complete a range of tasks that are similar to those done by larger computers. Sophisticated electronic calculators can be programmed with complex mathematical formulas. Some models employ interchangeable preprogrammed software modules that are capable of 5 or more program steps, even though the data must still be keyed manually. Many units have a built-in printer or an additional one with graphing capabilities, while some models can draw mathematical equations. A lot of calculators come with basic computer games that are played on the calculator's display screen. The distinction between calculators, PDAs, personal digital assistants (PDAs) and portable computers has been blurred due to the fact that all of these devices now typically use microprocessors.
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