The earliest known calculating device is probably the abacus. It dates back at least to 1100 BC and is still in use today, particularly in Asia. Now, as then, it typically consists of a rectangular frame with thin parallel rods strung with beads. (See photograph.) Long before any systematic positional notation was adopted for the writing of numbers, the abacus assigned different units, or weights, to each rod. This scheme allowed a wide range of numbers to be represented by just a few beads and, together with the invention of zero in India, may have inspired the invention of the Hindu-Arabic number system. In any case, abacus beads can be readily manipulated to perform the common arithmetical operations—addition, subtraction, multiplication, and division—that are useful for commercial transactions and in bookkeeping.
The abacus is a digital device; that is, it represents values discretely. A bead is either in one predefined position or another, representing unambiguously, say, one or zero.
from Napier's logarithms to the slide rule
Calculating devices took a different turn when John Napier, a Scottish mathematician, published his discovery of logarithms in 1614. As any person can attest, adding two 10-digit numbers is much simpler than multiplying them together, and the transformation of a multiplication problem into an addition problem is exactly what logarithms enable. This simplification is possible because of the following logarithmic property: the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. By 1624 tables with 14 significant digits were available for the logarithms of numbers from 1 to 20,000, and scientists quickly adopted the new labour-saving tool for tedious astronomical calculations.
Most significant for the development of computing, the transformation of multiplication into addition greatly simplified the possibility of mechanization. Analog calculating devices based on Napier's logarithms—representing digital values with analogous physical lengths—soon appeared.
Pascal’s adding machine
The first calculator or adding machine to be produced in any quantity and actually used was the Pascaline, or Arithmetic Machine (see photograph), designed and built by the French mathematician-philosopher Blaise Pascal between 1642 and 1644. It could only do addition and subtraction, with numbers being entered by manipulating its dials. Pascal invented the machine for his father, a tax collector, so it was the first business machine, too (if one does not count the abacus). He built 50 of them over the next 10 years.
In 1671 the German mathematician-philosopher Gottfried Wilhelm von Leibniz designed a calculating machine called the Step Reckoner. (It was first built in 1673. See photograph.) The Step Reckoner expanded on Pascal's ideas and did multiplication by repeated addition and shifting.
Leibniz was a strong advocate of the binary system. Binary numbers are ideal for machines because they require only two digits, which can easily be represented by the on and off states of a switch. When computers became electronic, the binary system was particularly appropriate because an electrical circuit is either on or off. This meant that on could represent true, off could represent false, and the flow of current would directly represent the flow of logic.
Leibniz was prescient in seeing the appropriateness of the binary system in calculating machines, but his machine did not use it. Instead, the Step Reckoner represented numbers in decimal form, as positions on 10-position dials.
The Jacquard loom
The Jacquard loom was a marvel of the Industrial Revolution. A textile-weaving loom, it could also be called the first practical information-processing device. The loom worked by tugging various-coloured threads into patterns by means of an array of rods. By inserting a card punched with holes, an operator could control the motion of the rods and thereby alter the pattern of the weave. Moreover, the loom was equipped with a card-reading device that slipped a new card from a prepunched deck into place every time the shuttle was thrown so that complex weaving patterns could be automated.
Babbage’s Difference Engine.
Charles Babbage, a professor of mathematics, developed a machine called Difference Engine in the year 1822. This machine was expected to calculate logarithm tables to a high degree of precision. The difference engine was made to calculate various mathematical functions. The machine was capable of polynomial evaluation by finite difference and its operation was automatic multistop operation.
Babbage’s Analytical Engine.
The Analytical Engine was to be a general-purpose, fully program-controlled, automatic mechanical digital computer. It would be able to perform any calculation set before it. Before Babbage there is no evidence that anyone had ever conceived of such a device, let alone attempted to build one. The machine was designed to consist of four components: the mill, the store, the reader, and the printer. These components are the essential components of every computer today. The mill was the calculating unit, analogous to the central processing unit (CPU) in a modern computer; the store was where data were held prior to processing, exactly analogous to memory and storage in today's computers; and the reader and printer were the input and output devices.
Herman Hollerith's census tabulator
In 1877, an American named Herman Hollerith (1869-1926) fabricated what was dreamt by Charles Babbage. He fabricated the first electromechanical punched card tabulator that used punched cards for input, output and instructions. This machine was used by American Department of Census to compile their 1880 census data and were able to complete compilation in 3 years which used to take around 10 years.
Prof. Howard Aiken (1900-19973) in U.S.A constructed in 1943 an electromechanical computer named Mark-I which could multiply two 10-digit number in 5 seconds (a record at that time). Mark-I was the first machine which could perform according to pre-programmed instructions automatically without any manual interference. This was the first operational general purpose computer.