calculators
INTRODUCTION
Electronic, electromechanical electronic or electromechanical devices that perform mathematical operations automatically are known as calculators. Calculators perform calculations using the fundamental Arithmetic functions, including subtraction, multiplication, and division--and many can also perform more complex calculations, including usual and inverse trigonometric operations ( see trigonometry). The few innovations of the past decade have had as significant an influence on our lives such as the handheld, or pocket electronic calculator. These calculators can be used to help save time as well as to decrease the risk of making errors and are found wherever individuals are frequently in contact with numbers, such as stores, offices, banks and schools, labs, as well as in private homes.
The earliest calculators were mechanical: they ran their calculations with components of machines, such as disks, gears, and drums. These were powered by hand or later by electricity. In the 1950s, many machines such as these calculators were replaced by electronic calculators which had integrated circuits -- in some cases similar the ones in computers, to provide mathematical functions. In fact, the sophisticated electronic calculators that we have today are specifically designed, or even special-purpose computers. They contain built-in instructions on how to use certain operations.
Like other computer systems, calculators are of two types--analog and digital. Analog calculators are able to work with variable physical quantities--fluid flow or voltages, for example--and solve mathematical problems by creating an analogy in physical form to the issue. Clocks, slide rules, and utilities meters can be all examples that are analog calculators. Digital calculators include the tools most often considered calculators. They are directly based on numbers , digits or numbers and operate by counting, listing as well as comparing these numbers. Digital calculators include adding machines, cash registers and handheld or desktop electronic calculators.
PRINCIPLES OF MECHANICAL CALCULATORS
The fundamental part of all mechanical calculators is a set numeral-adding wheels. For a mechanical calculator driven by keys (and in most others) they are visible through a row of small window on the side and back of the unit. Each wheel has the numerals in the range 0-9, which are engraved on its rim. Behind each wheel, there is a column of keys engraved with the same numbers. Pressing the 1 key in a column makes its numeral wheel by one step. depressing the number 2 key spins the wheel for two steps, and so on. When the keys 1 and 2 are simultaneously pressed it will move the wheel one step, and after that two moresteps, finally signalling 3. A column of numbers may be added rapidly by typing the numbers into the keyboard and then reading their sum in the windows. Interlocking mechanisms between numeral wheels automatically provide for carryovers. Multiplication is performed by repeated subtraction; addition is carried out with an indirect method and division is achieved through repeated subtraction.
PRINCIPLES OF ELECTRONIC CALCULATORS
Electronic calculators are carried out by integrated circuits, tiny arrays with thousands or millions, of transistors. They contain permanent instructions for addition and subtraction, multiplication and division, and (in more sophisticated calculators) additional functions. The numbers that are entered by the user are temporarily stored in addresses, or locations, in the memory called random-access (RAM) which contains capacity for the numbers used and created at any moment in the calculation process. The numbers that are stored in these addresses are then processed by circuits that contain the instructions for mathematical operations.
HISTORY
The most ancient calculating aid is the abacus, which has been in use for many years. It consists of movable counters placed on an engraved board or hung on wires. The first version of the slide rule commonly referred to as the first analog calculator that was successful, was invented in 1620, through the English mathematician Edmund Gunter. Slide rules were initially utilized to multiply or divide numbers by adding or subtracting their logarithms. Later it became possible to make use of slide rules to calculate square roots, and in some instances, to calculate trigonometric operations and logarithms.
MECHANICAL CALCULATORS
The first digital mechanical calculating machine, the precursor to the modern calculator was an arithmetic machine devised by the French mathematician Blaise Pascal in 1642 ( see Pascaline). In the 17th century, Gottfried Wilhelm Leibniz created a more advanced design of Pascal's invention. It used a shaft with gradually longer teeth that were fixed to it , as well as a cogwheel sporting 10 teeth. The cogwheel's edges could be seen on a dial, and was marked with numbers 0 to 9. By positioning the cogwheel in an exact position along the shaft, and then turning the shaft, two numbers could be added. If you wanted to add two numbers by turning the shaft repeatedly. Subtraction was achieved through turning the shaft in reverse and division was accomplished by subtraction repeatedly.
In 1878 W.T. Odhner in 1878, invented the pin-wheel. When a number was set in a machine equipped with this device, the number of pins would be raised by wheels on the primary shaft. When the shaft was turned, the pins merged with cogwheels, and their movements gave the answer to the sum similarly to the way they did the cogwheels in Leibniz's machine. Invention of the pin wheel made it possible to make cleaner and more easily driven machines.
The first successful commercially-produced key-driven calculatorthat was later named the Comptometer was invented by Dorr Eugene Felt in 1886. Key-driven calculators were able to be operated fast and were often used in offices. In one kind of key-driven calculator, called a key-set device, the keypads for numbers were first depressed or then cocked. A subsequent action -- turning a crank or launching a drive motor--transferred the number put into the keyboard to the numeral wheels. Key-set principles were used to calculate machines that printed their results on the paper tape, since it was not possible to direct printers directly from the keys.
The first successful commercially-produced rotary calculator was invented by Frank S. Baldwin and Jay R. Monroe in 1912. The first rotary calculators included a rotary mechanism to transfer numbers stored on the keyboard onto the adding-wheel unit. Since the rotary drive lent itself to high-speed repeating addition and subtraction, these machines could multiply and divide very quickly and even automatically.
A special purpose mechanical calculators feature the cash register. This was invented in 1879 James Ritty, a storekeeper, to ensure the honesty of his clerks. The first bookkeeping equipment--a printing-addition device was invented in 1891 in 1891 by William S. Burroughs, the bank clerk. Punch-card machinesthat were originally designed for controlling the operation of weaving looms, were modified to processing information around the time of the 1800s. They were developed by Herman Hollerith of the United States Bureau of the Census. They read data from cards where patterns of holes represented numbers and letters.
ELECTRONIC CALCULATORS
Electronics advancements during the 1940s and 1950s were instrumental in making possible the development of computers as well as the electronic calculator. Electronic desktop calculators that were first introduced in the 1960s, fulfilled the similar functions to the rotary calculators but they were without moving parts. The development of miniature electronic devices that were solid-state brought about a series of electronic calculators which could perform greater functions and quicker operation than their mechanical predecessors. Today , the majority of mechanical calculators have been replaced with electronic models.
The latest handheld electronic calculators can do not only addition, subtraction, multiplication, and division but also can deal with square roots, squaring, and percentages when the correct key is pressing. The input data and the end result are displayed on screens using either light-emitting diodes (LEDs) or liquid crystal display (LCDs).
Special-purpose calculators have been designed to use in engineering, business as well as other fields. Some are able to complete a range of work similar to those done by larger computers. Sophisticated electronic calculators are able to be programmed using complicated mathematical formulas. Certain models come with interchangeable software modules that are capable of thousands or more of program steps, but the required data needs to be entered manually. There are many calculators that have a built-in or accessory printer with graphing capabilities, while some models can draw mathematical equations. Many calculators include rudimentary computer games that can be played directly on the calculator's screen. In reality, the line between calculators, PDAs, personal digital assistants (PDAs), and portable computers is blurred because all of these devices currently use microprocessors.
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