calculators
INTRODUCTION
Mechanical, electromechanical electronic or electromechanical devices that do mathematical calculations automatically are known as calculators. Calculators perform calculations using the basic Arithmetic operations--subtraction, addition multiplicationand division. They can also perform more complex calculations, like indistinto trigonometric functions as well as inverse trigonometric ( see trigonometry). Few technological innovations in recent years have had as significant an influence on our lives as the handheld, also known as a pocket electronic calculator. These calculators can be used to help save time and reduce the risk of making errors and are used wherever there are people who frequently deal with numbers - in offices, retail stores, banks and laboratories, in schools, and even in homes.
The early calculators were mechanical: they made calculations using machine components, like disks, drums, and gears--that were powered via hand, and later electricity. The mid-1950s saw a number models of mechanical calculators were being replaced by electronic calculators which had integrated circuits, in some cases similar to those found in computers--to provide mathematical functions. In fact, the sophisticated electronic calculators of today are dedicated, or special-purpose, computers. They are equipped with instructions that tell you 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 instance. They also solve mathematical problems by creating an analogy physical to the problem. Slide rules, clocks, and utility meters are all examples that are analog calculators. Digital calculators comprise the gadgets most commonly thought of as calculators. They operate directly with numbers or digits , and operate by counting, listing, comparing, and rearranging these numbers. The most common digital calculators include adding machines, cash registers, and handheld or desktop electronic calculators.
PRINCIPLES OF MECHANICAL CALCULATORS
The most fundamental component of mechanical calculators comprises a set of numeral-adding wheels. For a mechanical calculator driven by keys (and in most others) the wheels can be viewed through the rows of small windows on the front part of the instrument. Each wheel is adorned with the numbers 0 through 9 marked around its edge. Behind each wheel, there is a column of keys that are marked with identical digits. The number 1 key in a column spins the numeral wheel one step; depressing the number 2 key rotates the wheel by two steps and then on. When the 1 and 2 keys are repeatedly pressed each time, the wheel is moved forward one step and then two steps further, before finally indicating three. Thus a column of numbers may be added rapidly by typing the numbers on the keyboard, and then reading their totals in the windows. Interlocking mechanisms between numeral wheels automatically enable carrying overs. Multiplication is achieved by repeated addition; subtraction is done with an indirect method and division is achieved through repeated subtraction.
PRINCIPLES OF ELECTRONIC CALCULATORS
The operation of electronic calculators can be performed using integrated circuits--tiny arrays of thousands, or millions, of transistors. These circuits include permanent instructions for subtraction, subtraction, multiplication, division and (in more sophisticated calculators) other functions. The numbers entered by the operator are temporarily stored in addresses, or locations in the random-access memory (RAM) which contains enough space to store the numbers that are used and produced at any given time by the calculator. The numbers stored in these addresses are then processed by circuits that hold the instructions for the mathematical operations.
HISTORY
The oldest method of calculation is the abacus. It has been in use for a number of many thousands of years. It consists of movable counters that are placed on a marked board or strung along wires. An early version of the slide rule commonly referred to as the first ever successful analog calculator was designed in 1620 through the English mathematician Edmund Gunter. Slide rules were initially used to divide or multiply numbers by subtracting or adding their logarithms. Later , it was possible make use of slide rules in order to extract square roots and, in some instances, to calculate trigonometric function and logarithms.
MECHANICAL CALCULATORS
The first digital mechanical calculator, which was the predecessor to the modern calculator was an arithmetic machine invented by French mathematician Blaise Pascal in 1642 ( see Pascaline). Later in the 17th century Gottfried Wilhelm Leibniz created a more advanced model of the machine that Pascal had designed. It utilized a shaft with increasing length of teeth, which were fixed to it , as well as a cogwheel sporting 10 teeth. The cogwheel's edge could be seen on a dial, and was marked with numbers 0-9. When the cogwheel was positioned in a specific direction along the shaft, and then turning the shaft the shaft, two numbers could be added. For the purpose of multiplying two numbers, the shaft was rotated repeatedly. Subtraction was accomplished via turning the shaft backward, and division was performed through subtraction repeated.
In 1878 W.T. Odhner invented the pin-wheel. When an amount was set on a machine using this device, the number of pins would be placed on wheels mounted on the main shaft. When the shaft was turned, the pins became locked with cogwheels, and their movements gave the answer to the sum similar to how they did those in Leibniz's machine. This invention of the pin-wheel was what made it possible to build simpler and more efficient machines.
The first successful commercially-produced key-driven calculator, later called the Comptometer was created by Dorr Eugene Felt in 1886. Key-driven calculators were able to be operated rapidly and were widely used in offices. In a particular type of key-driven calculator, called key-set machines, the number keys were first pressed, or then cocked. Then , a second action--turning the crank or launching an electric motor -- transferred the number input into the keyboard and to the numeral wheels. The principle of key-set was employed in calculating machines that printed results on the paper tape, since it was not possible to control printers directly using the keys.
The first successful commercially-produced rotary calculator was developed by Frank S. Baldwin and Jay R. Monroe in 1912. The first rotary calculators featured a rotary mechanism to transfer numbers that were set on the keyboard into the adding-wheel unit. Because the rotary drive lends itself to high-speed repeated subtraction and addition the machines were able to increase and decrease quickly, and also automatically.
The special-purpose calculators comprise the cash register. It was invented in 1879 by James Ritty, a storekeeper to ensure the integrity of his employees. The first bookkeeping machine - an adding-printing device was invented in 1891 through William S. Burroughs, a bank clerk. Punch-card machinesoriginally employed to govern the operation of looms, were adapted 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 information by using cards on which patterns of holes symbolized numbers and letters.
ELECTRONIC CALCULATORS
Electronics advancements during the 1940s and 1950s made possible the creation of the computer as well as the electronic calculator. Electronic desktop calculators that were first introduced in the 1960s, had the same functions as rotating calculators but with virtually no moving components. The introduction of miniature electronic devices with solid-state electronics brought an array of electronic calculators which could perform much more functions and more efficient than their mechanical predecessors. Today , the majority of mechanical calculators have been replaced with electronic models.
These modern handheld electronic calculators can not only perform multiplication, subtraction, addition and division, but they also are able to handle square roots percentages, and squaring. These are all possible by pressing the appropriate key. press. The data being entered and the final results are displayed on the screen using either light-emitting diodes (LEDs) or liquid-crystal screens (LCDs).
Special-purpose calculators were developed for use in business, engineering and other areas. Some are able to manage a variety of tasks that are similar to those performed by larger computer. Electronic calculators are able to be programmed using complicated mathematical formulas. Certain models have interchangeable preprogrammed software modules capable of 5,000 or more program steps, although the data needs to be entered manually. A majority of models have built-in printer, or an optional one with graphing capabilities, while some models can draw mathematical equations. A lot of calculators include rudimentary computer games that can be played directly on the calculator's screen. The distinction between calculators, the personal digital assistants (PDAs) and portable computers has been blurred because all these devices generally use microprocessors.
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