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Base 3.1

3.1.1 Why do you need binary

When carrying on the arithmetic operation, it must involve the binary problem, for the computer, it also needs to carry on the arithmetic operation, so it must also involve the binary problem.

2.1.2 what is binary

The so-called base is the rule of data accumulation when the calculator (man / machine) performs arithmetic operations, such as the decimal system, its accumulation rule is that every ten into one, 0 to 9 is digital, but the digital symbols are different in different cultures, such as

(1) India / Arabia: 0 1 2 3 4 5 6 7 8 9, currently used all over the world

(2) one two three. Nine

(3) Chinese: zero one two three. Nine, or zero one or two. Jiu

(4) other:

3.1.3 in principle, it can have n (n > = 2) binary.

In principle, you can have n-base, n > = 2, so you can have 2, 3, 4, 5, 6, 7, 8, 8, 8, 16, and 20. N, for example, the current base is

(1) binary system: every 2 into 1, the number is 0pl

(2) Octal system: every 8 into 1, the number is 0, 1, 2, 3, 4, 5, 6, 7.

(3) Decimal system: every 10 into 1, the number is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

(4) hexadecimal system: every 16 into 1, the number is 0, the number is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

3.1.4 base is just a way to count

The same value can be represented in different bases, and the representation may be different. For example, the number 30 in decimal system is expressed in other bases.

(1) binary: 11110

(2) Octal: 36

(3) hexadecimal: 1e

Although the representation is different, the numerical value of the representation is equal.

3.1.5 which system is used by the user to count, which needs to be determined according to the characteristics of the user?

(1) for people

The base system used by people should not be too low or too high.

1) if the base is too low

If the binary is too low, it will lead to carry too often, the human brain can not respond, for example, binary carry will be very frequent, for people, the use of binary counting is not appropriate.

2) if the base is too high

For example, to get a base of 100, the carry is too slow, it needs to be carried every 100, it is really too slow.

3) it is suitable for people to use carry base which is neither fast nor slow.

For people, it is appropriate to use the hexadecimal system 8, 9, 10, 11, 12, 14, 15 and 15. For example, the Mayans are 12-ary, but humans are accustomed to using the decimal system, so they use the decimal system. Maybe it's because humans have ten fingers.

(2) Mechanical computer

For the early mechanical computers, because the mechanical running speed was slow, the base system was too low to lead to frequent carry, the mechanical speed could not keep up with it, and the base system was too high and led to carry too slow, so like people, the early mechanical computers, most of them also use decimal production as the computing base.

(3) Electronic computer

Due to the characteristics of electronic computers, people find that electronic computers are very suitable for the use of binary counting, and then we will introduce why suitable electronic computers are suitable for using binary counting.

3.2 Why do electronic computers (digital circuits) use binary?

3.2.1 binary

(1) for every 2 to 1, there are only 0 and 1 digits.

(2) the binary system has a very outstanding advantage, that is, the binary system has only two digits, namely 0 and 1, and the numbers are simple and easy to use in physical form, such as

1) A hole in the paper tape is 1, and no hole is 0.

2) 2.5v high voltage is 1pm 0v is 0

Unlike the decimal system, there are 0 and 7, 8, and 9 is a number. When expressed in physical form, you need to use ten states to represent the ten digits.

(3) binary system also has obvious disadvantages.

That is, binary carry is too fast, and as mentioned earlier, it is not suitable for slow calculators, such as people or early mechanical computers.

But for electronic computers that use electrical signals to work, because the speed of electronic computers is very fast, this disadvantage has no effect on electronic computers.

3.2.3 what are the advantages of using binary in electronic computers

(1) it is easy to use the dimorphism of electronic devices to represent binary 0,1 digits.

1) the so-called dimorphism is two states, and the circuit is full of dimorphism, such as high / low level, saturation / cut-off, on / off, etc., which is very suitable to represent the binary numbers 0 and 1.

2) in the circuit, the most common is to use high and low levels to denote 0x1, such as 0v (low level) for 0Rhon2.5v (high level) for 1.

(2) it is easy to permanently store binary data

1) early paper tape storage

Punch a hole in the paper tape, when the light shines on the paper tape, the light can pass through the hole and be received by the other side, it will die data 1, otherwise it will be data 0.

2) disk storage

The binary data is represented by the direction of the magnetic pole (positive and negative) to realize the permanent preservation of the data.

3) CD-ROM storage

The bump on the surface represents the 0Pax 1 of the binary data.

(3) it is easy to perform arithmetic and logical operations.

1) it is easy to realize arithmetic operation

It is easy to design the binary addition circuit (adder), and the core of the arithmetic operation unit is the adder. For the computer, as long as the addition operation is realized, other subtraction / multiplication / division operations can be extended from the addition operation.

2) it is easy to implement logical operations (and, OR, non)

There is a concept of true or false in logic operations (the condition is true and not true). The binary "1 Ture" can be used to represent "true" and "false", 1 can represent "true", and 0 can mean "False", so electronic computers use binary system, which is very suitable for logical operations.

The logical operation of the computer is also done by using the "adder".

(4) the electronic computer uses binary data and has strong anti-interference ability.

Because the binary number has only two states, such as 2.5v for 1j0v, the state is very simple, so it has strong anti-jamming ability. if it is a decimal system, ten states are needed to represent 0. 9 digits, the more complex the state is, the more likely it is for data to make errors due to interference.

This is like we usually deal with things, if things are very simple, even if a little interference is fine, it is not easy to make mistakes, if things are very complicated, even a little interference is easy to make mistakes.

Author: Jiajie Studio

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