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Dualistic history
1. Binary History (less than 150 words)1Leibniz, a German master of mathematical philosophy in the 8th century, read the composition of gossip from the Latin translation of Yijing sent to him by his missionary friend Bowitt, and was surprised to find its basic prime number (0)( 1), that is.

In the 20th century, the invention and application of computers, known as one of the important symbols of the third scientific and technological revolution, had a binary operation mode. It not only proves that Leibniz's principle is correct, but also proves that the mathematical theory of the Book of Changes is great.

1672, 1 In June, Leibniz made a wooden machine model and showed it to the members of the Royal Society. But this model can only explain the principle and can't work normally. Since then, in order to speed up the process of developing computers, Leibniz lived in Paris for four years. In Paris, he cooperated with the famous watchmaker Olivier. He just needs to make a simple explanation to olivet, and the actual manufacturing work will be done by the watchmaker alone. 1674, the final machine was assembled by Hollibert alone. Leibniz's multiplier is about 1 meter long, 30 cm wide and 25 cm high. It consists of a fixed counter and a movable positioning mechanism. The whole machine is driven by gear system, and its important part is stepped shaft, which is convenient for simple multiplication and division operation.

The prototype of Leibniz's design was exhibited in Paris and London. Because of his outstanding achievements in computing equipment, he was elected as a member of the Royal Society. 1700 was elected as an academician of the Paris Academy of Sciences.

When Leibniz settled in France, he had close contact with Bai Jin, a missionary to China. Bai Jin once taught a math class to Emperor Kangxi. He is very interested in China's Book of Changes. 170 1 year, he gave Leibniz two maps of Yijing, one of which is the famous orientation map of Fuxi's sixty-four hexagrams. Leibniz was surprised to find that these sixty-four hexagrams correspond to sixty-four binary numbers. Leibniz thinks that China's gossip is the earliest binary notation in the world. Therefore, Leibniz yearns for and admires the ancient civilization of China. He presented the replica of his instrument to Emperor Kangxi of China to show his respect for China.

2. The reason why computers use binary system is that binary system has the following advantages: (1) It is easy to be realized technically.

Binary digits 0 and 1 can be easily represented by bistable circuits. Computers use binary codes instead of the familiar decimal codes. The most important reason is that binary code is physically easier to implement.

Because most electronic devices have two stable states. For example, the transistor is turned on and off, the voltage is high or low, and there is no magnetism.

It is difficult to find an electronic device with ten stable states. The advantage of using binary is that it is simple to operate.

There are 55 arithmetic rules of summation and quadrature in decimal system and only 3 in binary system, which can simplify the design of physical devices such as arithmetic unit. In addition, the computer has fewer components, which can enhance the stability of the whole system.

Interestingly, when the first computer ENIAC was developed, the designers used decimal counting. The method is to group every ten transistors, one of which represents decimal 1 bit. This clumsy method caused von Neumann to think, and he put forward the idea of storing program data in binary.

This greatly reduces the number of components in the computer and improves the running efficiency. Therefore, binary is a natural choice for computers.

(2) High reliability. Binary only uses 0 and 1, which is not easy to make mistakes in transmission and processing, and ensures the high reliability of the computer.

(3) The operation rules are simple. Compared with decimal numbers, the operation rules of binary numbers are much simpler, which not only simplifies the structure of operators, but also helps to improve the operation speed.

(4) Consistent with logical quantity. Binary numbers 0 and 1 correspond to logical quantities "true" and "false", so it is very natural to represent binary logic with binary numbers.

(5) The conversion between binary numbers and decimal numbers is quite easy. People can still use the customary decimal number when using the computer. The computer automatically converts it into binary number for storage and processing, and then automatically converts the binary number into decimal number when outputting the processing result, which brings great convenience to the work.

3. The historical background of binary is binary, and 0, 1 is the basic operator; The basis of computer operation is binary.

Computers are based on binary, so what is binary and why do you need it? In the early design of mechanical computing device, decimal or other decimal was used instead of binary, and different positions of gears were used to represent different values. This computing device may be closer to the human way of thinking. For example, a computing device has ten gears, which are connected in stages. Each gear has ten squares, the pinion rotates once, and the big gear moves one square.

This is a simple decimal data representation device, which can represent numbers from 0 to 99999999999. With other mechanical equipment, such a simple gear-based device can realize simple decimal addition and subtraction.

This method of representing numerical values with different symbols in different positions is binary representation. The commonly used decimal system is mainly decimal system (because we have ten fingers, decimal system is a reasonable choice, and fingers can represent ten numbers. The concept of 0 did not appear until a long time later, so it is 1- 10 instead of 0-9).

After the appearance of electronic computers, it is too complicated to express ten states with electronic tubes, so all electronic computers have only two basic states, on and off. That is to say, the two states of the electron tube determine that the electronic computer based on the electron tube uses binary to represent numbers and data.

Octal and 16 are also commonly used. In computer science, 16 system is often used, but decimal system is rarely used. This is because the 16 system has a natural connection with the binary system: four binary digits can represent numbers from 0 to 15, which is exactly 1. The binary "00 10 1000" can be directly converted into the binary "38" of 16.

Words are the basic unit of storage in computers. Depending on the length of a computer word, a word has different digits. The word length of modern computers is generally 32 bits, that is to say, the number of bits in a word is 32. Bytes are 8-bit data units, and one byte can represent 0-255 data.

In modern computers with 32-bit word length, one word is equal to 4 bytes, and in early computers with 16 bits, one word is equal to 2 bytes.

4. The historical origin of binary arithmetic originated from Zhouyi at the beginning of 1000 BC. At first, it was mainly used for divination, and the two symbols in it may represent "yes" and "no" respectively. This book can only serve as a reference and inspiration for Leibniz's research. If binary originated in ancient China, Zhouyi is the origin of binary.

A precious manuscript entitled "1 and 0, the magical origin of all numbers" is preserved in the famous schloss ilios Kzugoda in Thuringia. This is an excellent example of creating secrets, because everything comes from God. "

This is the handwriting of Gottfried Wilhelm Leibniz (1646- 17 16). However, Leibniz has only a few pages of extremely refined description of this magical and wonderful digital system.

Leibniz's research results are closely related to an ancient book in China, which is the Book of Changes. China's Book of Changes uses hexagrams and hexagrams to represent all things in the world, in which hexagrams are the most basic elements. The hexagrams are divided into two types: yin hexagrams (represented by "-") and yang hexagrams (represented by "-"), and yin hexagrams and yang hexagrams.

Everything in the world has eight basic elements, namely, heaven, earth, thunder, wind, water, fire, mountains and mountains. They are represented by eight diagrams, namely, dry, Kun, earthquake, hurdle, separation, root and communication. When the eight diagrams are matched with each other, 64 hexagrams can be obtained, representing various natural phenomena and personnel phenomena. Let's compare the composition of binary: the number of bits of binary is 0, 1, and 3-bit binary can be combined into 8 states, which can be expressed as 0, 1.

7, two 3-bit binary numbers are combined into 6-bit binary numbers, that is, 2=64, that is, 64 states. Can gossip according to 0, 1,? The eight numbers are arranged as follows: 0- Kun (ground), 1- Root (mountain), 2- Kan (water), 3- Smoke (wind), 4- Earthquake (thunder), 5- Li (fire) and 6-.

If we further analyze the gossip, we can find that there are binary arithmetic and logical operations in the gossip, such as Gan Kun, Li Kan, Gen Dui and Zhen Xun. The binary logic operation between them is an anti-code relationship, which is philosophically opposite. Eight trigrams can be combined into sixty-four hexagrams. For example, the "Qian Gua" in the sixty-four hexagrams is composed of Kun Gua, and Kun is above the ground. This divination is a kind of "modest divination" phenomenon, and the gentleman follows its spirit and takes more and less.

If the sixty-four hexagrams are further evolved, there are: 64*64=4096 states. In this way, we can get various States between heaven and earth. In other words, we can study everything in the world through hexagrams.

The Book of Changes says: "Therefore, it is easy to have Tai Chi. Is to give birth to two instruments, two instruments give birth to four elephants, and four elephants give birth to gossip. Gossip is good and bad, and good and bad will lead to great cause. " "Heaven, one place and two places, three places and four places, five places and six places, seven places and eight places."

"There are six ways to do it. Kun's strategy is four tenths.

Where 300 has 60, which is the date of the current period. There are 1,520 policies in two chapters, and the number of things is also. "

Tai Chi here refers to the chaotic atmosphere in the universe. Two instruments are binary bits 0 and 1, four images are four states of two-bit binary combination, and eight diagrams are eight states of three-bit binary combination. "1520, when the number of everything is also" is the number obtained by binary operation, totaling 1520, which is equivalent to the number of everything.

It can be seen that the Book of Changes is a science that studies everything in the world through binary system, and it is the earliest origin and application of binary system. In Leibniz's eyes, this is China's copy of his binary, but actually Leibniz was influenced by China's Yin and Yang Taiji, but he did a lot of research and popularized the binary.

He felt that the relationship between this symbol system from China ancient culture and his binary system was too obvious, so he asserted that the binary system was the most perfect universal logic language in the world. But what we need to know is that it is unrealistic to try to link the binary system with the Book of Changes in ancient China.

But even Leibniz didn't think that his binary mathematics pointed not to ancient China, but to the future. Leibniz recorded his binary system in his diary in March 1679, and at the same time, he designed a machine that can complete digital calculation.

Today's modern technology has turned this idea into reality, which was unimaginable in the Leibniz era. Extended data:

The advantage of computer using binary: 1, which is easy to realize in the circuit: when the computer is working, the circuit is electrified, so each output terminal has a voltage.

The voltage level is converted into binary by analog-to-digital conversion: the high level is represented by 1 and the low level is represented by 0. That is, analog circuits are converted into digital circuits.

The height here can be determined artificially. Generally, below 2.5 volts is low level, and above 3.2 volts is high level. There are only two binary digits (0 and 1).

As long as the circuit can identify low and high, it can represent "0" and "1". 2. Easiest physical storage: (1) Basic principle: binary is the easiest physical storage, and it is recorded by the orientation of magnetic poles, the unevenness of the surface, the presence or absence of illumination, etc.

(2) The specific truth: For a write-once optical disc, the laser beam is converged into a small beam of 1-2 um, and the tellurium alloy film on the surface of the optical disc is melted by the action of heat, forming a small hole (pit) on the film, recording "1" and recording "0" in the original position indication. 3. It is convenient for addition, subtraction and counting coding.

Easy to convert, binary numbers and decimal numbers are easy to convert each other. Simplified operation rules: There are three combinations of sum and product operations of two binary numbers, and the operation rules are simple, which is conducive to simplifying the internal structure of the computer and improving the operation speed.

Electronic computers can process and process information at a very high speed, including data processing and processing, and have great information storage capacity. The data is represented by the physical state of the equipment in the computer, and the binary number system is adopted. All characters or symbols processed by a computer should also be represented by binary codes.

The advantages of using binary system are easy expression, simple operation rules and saving equipment. Elements with two stable states are known.

5. The historical origin of binary arithmetic Leibniz was also the first person to realize the importance of binary notation and systematically put forward binary number arithmetic.

Binary system has had a far-reaching impact on the development of computers after more than 200 years. 17 16 published "On China's Philosophy", focusing on gossip and binary, pointing out that binary and gossip have similarities.

1672, 1 In June, Leibniz made a wooden machine model and showed it to the members of the Royal Society. But this model can only explain the principle and can't work normally.

Since then, in order to speed up the process of developing computers, Leibniz lived in Paris for four years. In Paris, he cooperated with the famous watchmaker Olivier.

He just needs to make a simple explanation to olivet, and the actual manufacturing work will be done by the watchmaker alone. 1674, the final machine was assembled by Hollibert alone.

Leibniz's multiplier is about 1 meter long, 30 cm wide and 25 cm high. It consists of a fixed counter and a movable positioning mechanism.

The whole machine is driven by gear system, and its important part is stepped shaft, which is convenient for simple multiplication and division operation. The prototype of Leibniz's design was exhibited in Paris and London.

Because of his outstanding achievements in computing equipment, he was elected as a member of the Royal Society. 1700 was elected as an academician of the Paris Academy of Sciences.