calculators
INTRODUCTION
Electronic, electromechanical electronic devices that execute mathematical operations automatically are called calculators. Calculatorsperform calculations using the essential mathematical functions like subtraction, addition, division, and multiplication. Many can also perform more intricate calculations, including ordinário and inverse trigonometric operations ( see trigonometry). There are few inventions that have had such a profound influence on our daily lives like the handheld, or pocket, electronic calculator. These calculators can be used to help save time and to reduce the risk of making errors and can be found in places where there are people who frequently deal with numbers - in office spaces, in banks, stores and schools, labs, and even in homes.
The earliest calculatorswere mechanical. they ran their calculations with machine components, like disks, drums, and gears--that were powered by hand , or later, by electricity. In the 1950s, many were mechanical calculators were replaced with electronic calculators that contained integrated circuits -- in some cases similar the ones found in computers to accomplish mathematical calculations. In actuality, the highly-technical electronic calculators of today are specially-purpose computers. They have built-in instructions for how to use certain tasks.
As with other processing systems for data, calculators are of two types--analog and digital. Analog calculators utilize fluid flow or voltages, for instance. They solve math-related problems by constructing physical analogies to the problem. Clocks, slide rules, as well as utility meters, are examples from analog calculators. Digital calculators include the devices most frequently thought of as calculators. They are directly based on numbers or digits , and operate by listing, counting as well as comparing the numbers. A common set of digital calculators include adding machines, cash registers and desktop or handheld electronic calculators.
PRINCIPLES OF MECHANICAL CALCULATORS
The basic part of most mechanical calculators is a set numeral-adding wheels. In a key-driven mechanical calculator (and in the majority of others) the wheels can be viewed through a row of window on the side of the machine. Each wheel has the numerals of 0 through 9 around the edge. Under each wheel is a column of keys that are marked with the same numerals. Pressing the number 1 key in a column rotates its numeral wheel one step. pressing the number 2 key will rotate the wheel 2 steps and it goes on. When the 1 and 2 keys are used in sequence then the wheel will advance one step, and after that two steps further, before finally indicating 3. Therefore, a column of numbers could be quickly added by simply entering the numbers on the keyboard and observing their totals in the windows. Interlocking mechanisms between the numeral wheels automatically ensure carryovers. Multiplication is achieved by repeated addition. Subtraction is accomplished via indirect methods and division is accomplished by repeated subtraction.
PRINCIPLES OF ELECTRONIC CALCULATORS
The functions of electronic calculators are performed by integrated circuits--tiny arrays that comprise thousands or even millions of transistors. They contain permanent instructions for addition or subtraction, multiplication or division, and (in more sophisticated calculators) additional functions. The numbers that the operator enters are briefly stored in addresses, or locations, in the memory called random-access (RAM), which has space for the numbers used and produced at any given moment in the calculation process. The numbers stored in these addresses are then processed by the circuits which carry instructions to perform the mathematical operations.
HISTORY
The oldest calculator is the abacus, which has been in use for a number of hundreds of years. It consists of movable counters, which are either placed on a marked board or hung on wires. An early version of the slide rule often regarded as the first digital calculator that worked, was developed in 1620 by the English mathematician Edmund Gunter. This rule initially used to divide or multiply numbers by adding or subtracting their logarithms. It was later possible to employ slide rules for calculating square roots as well as, in certain instances, to calculate trigonometric function and logarithms.
MECHANICAL CALCULATORS
The first mechanical digital calculating machine, the precursor to the modern calculator was an arithmetic machine designed by French mathematician Blaise Pascal in 1642 ( see Pascaline). In the 17th century Gottfried Wilhelm Leibniz created a more advanced variation of Pascal's machines. It employed a shaft with gradually longer teeth that were fixed to the cogwheel, and 10 teeth. The edge of the cogwheel could be seen on a dial, and was marked with the numbers 0 to 9. By putting the cogwheel a particular direction on the shaft and then rotating the shaft in a certain direction, two numbers can be added. For the purpose of multiplying two numbers the shaft was turned repeatedly. Subtraction was accomplished by turning the shaft in reverse and division was accomplished with subtraction that was repeated.
In 1878 W.T. Odhner developed the pin-wheel. When a number was determined on a machine using this device, the number of pins were raised on wheels carried on the shaft. When the shaft turned, the pins became locked with cogwheels, and their movements gave the answer to the equation in the same manner as did those on Leibniz's machines. This invention of the pin-wheel made possible to make sleeker and easier to drive machines.
The first key-driven calculatorthat was later named the Comptometer, was invented by Dorr Eugene Felt in 1886. Key-driven calculators could be operated rapidly and were widely used in offices. In one kind of key-driven calculatorknown as a key-set machine keypads for numbers were first depressed, or moved to cock. A second action, turning a crank or turning on an engine--transferred the numbers put into the keyboard to the numeral wheels. The key-set principle was used for calculating machines that printed their results on paper tape as it was not possible to control printers directly using the keys.
The first commercially successful Rotary calculator was created by Frank S. Baldwin and Jay R. Monroe in 1912. Rotary calculators featured a rotary mechanism that transferred numbers from the keyboard to the adding-wheel unit. Since the rotary drive lent itself to high-speed repeating addition and subtraction and division, these machines were able to increase and decrease quickly, and also automatically.
Mechanical calculators include the cash register. The cash register was invented in 1879 James Ritty, a storekeeper, to ensure the honesty of his clerks. The first bookkeeping machine--an adding-printing device -- was developed in 1891 by William S. Burroughs, one of the bank's clerks. Punch-card machinesoriginally employed to regulate the operation weaving looms, were modified to processing information during the 1880s, by Herman Hollerith of the United States Bureau of the Census. They read data from cards whose patterns of holes symbolized numbers and letters.
ELECTRONIC CALCULATORS
Developments in electronics in the 1940s and 1950s made possible the creation of the computer and the electronic calculator. Electronic desktop calculators were introduced in the 1960s, had the same function as mechanical calculators but they were without moving components. The advent of tiny electronic devices that were solid-state brought about a series of electronic calculators with many more functions and more speed than their mechanical predecessors. Today , the majority of mechanical calculators have been replaced by electronic models.
Contemporary handheld electronic calculators can do not only multiplication, subtraction and division, but are able to handle square roots percentages, and squaring. All this is accomplished when the correct key is pressed. The data entered as well as the result are shown on a screen with or light emitting diodes (LEDs) or liquid crystal displays (LCDs).
Special-purpose calculators have been developed for use in engineering, business and other fields. Some of them are able to handle sequences of tasks much like the ones performed by larger computers. Sophisticated electronic calculators can be programmed using complex mathematical formulas. Certain models use interchangeable preprogrammed software modules that can perform up to 5,000 or more steps, even though the information must be entered manually. Many units have a built-in printer or an additional one and some even graph mathematical equations. Many calculators contain basic computer games that are played on the calculator's screen. In fact, the distinction between calculators and personal digital assistants (PDAs) and portable computers has been blurred because all of them generally use microprocessors.
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