The storage and operation of data in computers use "binary". Because binary numbers only have two basic symbols, "0" and "1", and computers are composed of logic circuits, logic circuits usually only have two states, the switch is on and off, and "1" can be used for these two states. and "0" indicates.
#Data in the computer is represented in binary. Data in computers can be divided into two categories according to their basic uses: numerical data and non-numeric data. Numerical data represents a specific quantity, which can be divided into positive and negative sizes. Non-numeric data mainly includes characters, sounds, images, etc. This type of data needs to be converted into binary representation using a specific encoding method before being stored and processed in the computer.
(1). The concept of base system
The base system is also the carry system, which is a carry method prescribed by people. For any base system - the X base system, it means that the number at a certain position is carried out by one digit every X. The decimal system advances by one after every tenth, the hexadecimal system advances by one after every hexadecimal, and the binary system advances by one after every two.
In a number system that uses carry counting, if only r basic symbols are used to represent values, then It is called the r-base (Radix-r Number System), and r is called the base (Radix) of the number system. The common characteristics of different number systems are as follows:
(1) Each number system has a certain set of symbols. For example, the decimal number system has ten basic symbols: 0,1,2...,9. There are two basic symbols of the binary number system: 0 and 1.
(2). Each number system uses positional representation. That is, the values represented by the symbols in different positions are different, which are related to the weight of their position.
For example: 1234.55 in decimal can be expressed as
1234.55=1×10^3 2×10^2 3×10^1 4×10^0 5×10^(-1) 5 ×10^(-2)
It can be seen that the value of the weight in various carry counting systems is exactly a certain power of the base. Therefore, any number represented by a carry counting system can be written as a polynomial expanded according to weights.
(2) Why do we use binary in computers?
The use of binary in computers is determined by its implementation mechanism. We can understand it this way: the basic components of a computer are composed of integrated circuits, and these integrated circuits can be regarded as composed of gate circuits (of course, in fact it is not that simple).
When the computer is working, the circuit is powered on, so there is voltage at each output end. The voltage level is converted into binary through analog-to-digital conversion: high level is represented by 1, and low level is represented by 0. That is to convert analog circuits into digital circuits. The high level and low level here can be determined artificially. Generally, the low level is below 2.5 volts, and the high level is above 3.2 volts. Electronic computers can process and process information at extremely high speeds. , including data processing and processing, and has great information storage capabilities. Data is represented in the computer by the physical state of the device, using a binary number system. All characters or symbols processed by the computer must also be represented by binary encoding. The advantages of using binary are that it is easy to express, the operation rules are simple, and it saves equipment. People know that components with two stable states (such as the on and off of transistors, on and off of relays, the level of electrical pulses, etc.) are easy to find, but it is necessary to find components with 10 stable states to correspond Decimal 10 numbers are difficult
1) The technology is simple to implement. Computers are composed of logic circuits. Logic circuits usually only have two states, the switch is on and off. These two states can be used "1" and "0" are represented. (2) Simplified operation rules: There are three combinations of sum and product operations of two binary numbers. The operation rules are simple, which is conducive to simplifying the internal structure of the computer and improving the operation speed. (3) Suitable for logical operations: Logical algebra is the theoretical basis for logical operations. There are only two digits in binary, which coincides with "true" and "false" in logical algebra. (4) Easy to convert, binary and decimal numbers are easy to convert to each other. (5) Using binary to represent data has the advantages of strong anti-interference ability and high reliability. Because each bit of data has only two states: high and low, when it is disturbed to a certain extent, it can still be reliably distinguished whether it is high or low.
(3), the reason why octal and hexadecimal appear
The general way of human thinking is expressed in decimal, while computers are expressed in binary, but for programmers, We need to deal directly with the calculator, if we are given a large series of binary numbers. For example, a 4-byte int type data: 0000 1010 1111 0101 1000 1111 11111 1111. I think any programmer will be very upset when seeing such a large string of 0s and 1s. So there must be a more concise and flexible way to present this pair of data.
You may say, just use decimal. If that is the case, it cannot accurately express the way of computer thinking (binary). Therefore, octal and hexadecimal have appeared. In fact, hexadecimal is more widely used. For example, if the above int type data is directly converted to octal, 32./3 remainder 2 means that we have to add 0 in front, but it is different when converted to hexadecimal. 32/4=8, written directly as a string of 8 hexadecimal values, simple and clear.
So using hexadecimal to express binary strings is undoubtedly the best way, which is why octal and hexadecimal appear.
(4), the problem of mutual conversion between base systems
Commonly used base systems are binary, decimal, octal and hexadecimal
Conclusion between binary and decimal Conversion
Decimal to binary
The method is: divide the decimal number by 2 and take the remainder method, that is, divide the decimal number by 2, the remainder is the number in the weight position, and the obtained quotient value continues to be divided by 2, as follows This step continues until the quotient reaches 0.
(The specific usage is as shown below)
Binary to decimal conversion
The method is: expand the binary numbers according to the weight and add them up to get Decimal.
(The specific usage is as shown below)
Conversion between binary and octal
Binary to octal
Method It is: 3-digit binary numbers are added according to weight expansion to obtain 1-digit octal number. (Note: when converting 3-digit binary to octal, the conversion starts from right to left, and 0 is added when insufficient).
(The specific usage is as shown below)
Convert octal to binary
The method is: the octal number is divided by 2 and the remainder is obtained. Binary number, for each octal number, there are 3 binary numbers, and if there are insufficient numbers, zeros are added to the leftmost number.
(The specific usage is as shown below)
Conversion between binary and hexadecimal
Binary to hexadecimal
The method is: similar to the method of converting binary to octal. Octal converts three into one, and hexadecimal converts four into one. (Note, the conversion from 4-digit binary to hexadecimal is from right to left, and 0 is added when insufficient).
(The specific usage is as shown below)
Hexadecimal to binary
The method is: divide the hexadecimal number by 2 Use the remainder method to obtain a binary number. Each hexadecimal number is 4 binary numbers. If there is insufficient number, zeros are added to the leftmost number.
(The specific usage is as shown below)
Conversion between decimal, octal and hexadecimal
Convert decimal to octal or decimal There are two methods of hexadecimal
First: indirect method-convert decimal to binary, and then convert binary to octal or hexadecimal. There will no longer be any explanation of how to use pictures here.
Second: Direct method - Convert decimal to octal or hexadecimal by dividing by 8 or 16 and taking the remainder until the quotient is 0.
(The specific usage is as shown below)
Convert octal or hexadecimal to decimal
The method is: convert octal and hexadecimal The decimal number can be obtained by expanding the base numbers according to weight and adding them.
(The specific usage is as shown below)
Conversion between hexadecimal and octal
Between octal and hexadecimal There are two methods for conversion between them
The first one: the conversion between them can be converted to binary first and then converted to each other.
Second type: The conversion between them can be converted to decimal first and then converted to each other.
There will be no further explanation of picture usage here.
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