calculators
INTRODUCTION
Electronic, electromechanical electronic devices which can perform math-related calculations automatically are called calculators. Calculators perform the standard arithmetic functions--addition, subtraction, multiplicationand division. They are also capable of performing more complex calculations, such as corrente and inverse trigonometric function ( see trigonometry). The few innovations of the past decade have had as profound an influence on the daily routine such as the handheld, or pocket electronic calculator. These calculators are used to save time as well as to decrease the chance of making mistakes and are found wherever people deal frequently with numbers--in banks, offices, shops and schools, labs, and homes.
The early calculators were mechanical. they made calculations using components of machines, such as disks, gears, and drums. These were powered by hand or later by electricity. Around the middle of the 1950s, many the mechanical calculators were replaced by electronic calculators which were equipped with integrated circuits--in certain cases, similar to the ones in computers, to provide mathematical functions. In reality, the modern electronic calculators nowadays are specially-purpose computers. They contain built-in instructions on how to execute certain operations.
Like other data-processing systems, calculators are of two kinds: analog and digital. Analog calculators operate with variables in physical quantities, like fluid flow or voltages, as an example. They solve mathematical problems by creating physical analogies to the problem. Clocks, slide rules or utility meters are all examples that are analog calculators. Digital calculators include the tools most often considered calculators. They deal directly with the numbers or digits. They function by listing, counting while comparing and then rearranging the numbers. Most digital calculators include cash registers, adding machines and desktop or handheld electronic calculators.
PRINCIPLES OF MECHANICAL CALCULATORS
The fundamental part of all mechanical calculators are a set numeral-adding wheels. When a mechanical calculator is operated by a key (and in most others) these wheels are visible through the rows of small windows on the front part of the instrument. Each wheel has the numerals in the range 0-9, which are engraved on its rim. Below each wheel is a column of keys engraved with identical digits. Pressing the key 1 in a column turns its numeral wheel one step, pressing the number 2 key will rotate the wheel for two steps, and then on. When the keys 1 and 2 are repeatedly pressed then the wheel will advance one step, and then two more, and finally it will indicate the number 3. This means that a column can be added quickly by entering the numbers into the keyboard and reading their sum in the window. The locking mechanisms that connect the numeral wheels automatically ensure carryovers. Multiplication is carried out by repeating addition. Subtraction is achieved with an indirect method and division is achieved through repeated subtraction.
PRINCIPLES OF ELECTRONIC CALCULATORS
The electronic calculators can be performed using integrated circuits--tiny arrays comprising thousands, and millions of transistors. These circuits have permanent instructions for addition, subtraction, multiplication, division, and (in more advanced calculators) other functions. The numbers input by the operator are briefly stored in addresses or places, in the memory known as random-access (RAM) which is a storage room for the numbers entered and produced at any given moment by the calculator. The numbers that are stored in these addresses are then processed by circuits that contain the instructions to perform the mathematical operations.
HISTORY
The oldest calculating aid is the abacus, which was used for thousands of years. It is comprised of movable counters that are placed on a marked board or strung along wires. An early version of the slide rule frequently referred to as the very first analog calculator that was successful, was designed in 1620 with the help of the English mathematician Edmund Gunter. This rule originally utilized to multiply or divide numbers by subtracting or adding their logarithms. It was later possible to use slide rules to extract square roots, and in some instances, to calculate trigonometric function and logarithms.
MECHANICAL CALCULATORS
The first mechanical digital computing machine--the precursor of the modern calculator was an arithmetic machine developed by the French mathematician Blaise Pascal in 1642 ( see Pascaline). In the 17th century, Gottfried Wilhelm Leibniz created a more sophisticated design of Pascal's invention. It was based on a shaft that had progressively longer teeth fixed along the shaft and a cogwheel that had 10 teeth. The cogwheel's end was is shown on a dial. The cogwheel was marked with numbers 0-9. By putting the cogwheel an exact position along the shaft, and then turning the shaft the shaft, two numbers could be added. When multiplying two figures by turning the shaft repeatedly. Subtraction was done with the help of turning it in reverse and division was achieved through repeated subtraction.
In 1878 W.T. Odhner developed the pin-wheel. When a specific number was entered on a machine with this mechanism, the appropriate number of pins would be elevated on wheels that were carried by the primary shaft. When the shaft turned, the pins were locked with cogwheels, which turned their revolutions to give the answer to the equation in the same manner as did those of Leibniz's device. Invention of the pin-wheel has made it possible to construct simpler and more efficient machines.
The first commercially successful key-driven calculatorthat was later named the Comptometer was invented by Dorr Eugene Felt in 1886. Key-driven calculators were able to operate quickly and were commonly used in offices. For a specific type of key-driven calculator, known as key-set machines, the number keys were first depressed or turned off. A subsequent action -- turning a crank or the start of an engine--transferred the numbers input into the keyboard and to the wheels for numerals. The key-set concept was utilized in the calculation of machines that printed results on paperstape because it was not possible to directly drive printers from the keys.
The first commercially successful rotary calculator was invented by Frank S. Baldwin and Jay R. Monroe in 1912. The first rotary calculators were equipped with a rotary device to transfer numbers that were set on the keyboard to the adding wheel unit. Since the rotary drive lent itself to high-speed repeated addition and subtraction that these machines could be able to multiply and divide extremely quickly and automatically.
Specific-use mechanical calculators comprise the cash register, which was invented in 1879 James Ritty, a storekeeper to ensure the integrity of his clerks. The first bookkeeping machine--an adding-printing device--was made in 1891 in 1891 by William S. Burroughs, the bank clerk. Punch-card machines, originally used to govern the operation of looms, were adapted to information processing through the 1880s Herman Hollerith of the United States Bureau of the Census. They read information from cards on which patterns of holes were interpreted as numbers and letters.
ELECTRONIC CALCULATORS
Technology advancements in the 1940s and 1950s led to possible the creation of the computer as well as the electronic calculator. Electronic desktop calculators, introduced in the 1960s, were able to perform the same functions as mechanical calculators but with virtually no moving components. The advent of miniaturized solid-state electronic devices brought a series of electronic calculators that could carry out significantly more functions and faster performance than their mechanical predecessors. Today , the majority of mechanical calculators are being replaced with electronic models.
The latest handheld electronic calculators can not only perform addition, subtraction, multiplication and division, but they also can deal with square roots, percentages, and squaring. This is whenever the appropriate button is hit. The information entered and the end result are displayed on the screen using LEDs or either (LEDs) or liquid-crystal monitors (LCDs).
Special-purpose calculators were designed for applications in engineering, business, and other fields. Some of them are equipped to manage a variety of tasks that are similar to the work of larger computers. The most sophisticated electronic calculators can be programmed with complex mathematical formulas. Some models are equipped with interchangeable software modules with thousands or more of program steps, however the data has to be entered manually. Many units have a built-in or accessory printer, and some can graph mathematical equations. Many calculators come with basic computer games that are played directly on the calculator's screen. In reality, the line between calculators as well as personal digital assistants (PDAs) and portable computers has blurred because all of them generally use microprocessors.
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