**The**

**abacus**

**.**

The earliest known calculating device is probably theThe 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.

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.

**Analog calculators:**

**from Napier's logarithms to the slide rule**

Calculating devices took a different turn whenCalculating 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, orMost 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.**

Leibniz’s Calculator

In 1671 the German mathematician-philosopherLeibniz’s Calculator

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 theLeibniz 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.

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 aThe 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 mechanicalThe 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.**

**Mark-I**

**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.**
## 34 comments:

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A friend in need is a friend indeed. ....................................................

Necessity is the mother of invention.......................................................

how do u do?

文章很棒~感謝!!..................................................

great msg for me, thanks a lot dude˙﹏˙

友誼能增進快樂,減少痛苦..................................................

真正的友誼，有如健康失去時，始知其價值........................................

格主的部落格內容真豐富~~看得很開心 ....................................................

很棒的分享~如有打擾之處,敬請原諒！........................................

Many a true word is spoken in jest.............................................................

愛，拆開來是心和受兩個字。用心去接受對方的一切，用心去愛對方的所有。................................................................

Keep in contact. Good Luck..................................................

欣賞是一種美德~回應是最大的支持^^.................................................................

當一個人內心能容納兩樣相互衝突的東西，這個人便開始變得有價值了。............................................................

如果相遇.你會感到相知.那麼.有一種習慣叫做陪伴;如果陪伴.你會感到珍惜.那麼.有一種甜蜜叫做存在!..................................................................

人生匆匆-把握當下，支持鼓勵~事事如意~..................................................................

卡爾.桑得柏：「除非先有夢，否則一切皆不成。」共勉！..................................................................

這個部落格好好好~棒棒棒~~~..................................................................

Practice what you preach.............................................................

死亡是悲哀的，但活得不快樂更悲哀。. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Gods mill grinds slow but sure...................................................

Of two evils choose the least.............................................................

A crowd is not company.............................................................

良言一句三冬暖，惡語傷人六月寒。......................................................................

人不能像動物一樣活著，而應該追求知識和美德............................................................

愛情不是慈善事業，不能隨便施捨。......................................................................

要求適合自己的愛情方式，是會得到更多，還是會錯過一個真正愛你的人。..................................................................

雖天地之大，萬物之多，而惟吾蜩翼之知。..................................................

Pen and ink is wits plough...................................................................

成功可招引朋友,挫敗可考驗朋友......................................................................

一棵樹除非在春天開了花，否則難望在秋天結果。............................................................

正點喔 多謝大大無私的分享 感恩拉(￣∀￣)......................................................

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