【11】 Binary code: "holding two roller handcuffs, crying out for hot hot hot"?

【 The principle of computer organization 】 Learning notes —— General catalogue

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• Recommended reading ：《 code ： Language hidden behind computer hardware and software 》

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introduction

One 、 Understand binary “ On the two into one ”

• Binary conversion 10 Base number ： 0011【 Binary number 】, 0×23+0×22+1×21+1×20=3【0011 Corresponding decimal number 】

• 10 Turn into the system 2 Base number 【 Short division 】

  • such as , We want to 13 This decimal number , Convert to binary by short division , You need to go through the following steps ： therefore , The corresponding binary number , Namely 1101.
    

• Original code notation

  • Positive numbers ：0011【 representative 3, First place 0 For a positive number 】
  • negative ：1011【 representative -3, First place 1 It's a negative number 】
  • problem ：1000 and 0000 All represent 0, wasted 1 Number

• extraction Complement code 【 The first is 1 when , It's a negative number , To 10 Base time , Put a minus sign on the far left 】

  • example ： One 4 Binary complement value of bit 1011, Convert to decimal , Namely −1×23+0×22+1×21+1×20
  • The method of finding decimal complement 【 Add... In reverse 1】： -5 Corresponding to a signed bit negative number 5（10000101）→ All bits except sign bits are negated （11111010）→ Add 00000001 by (`11111011)0【-5 The complement of is 11111011】
  • Of course More important yes , Use a complement to show a negative number , Make our It's easy to add integers , There's no need to do anything special , Just add it as a normal binary , You can get the right results .
    

Two 、 Representation of a string , From coding to numbers

1、 ASCII code （American Standard Code for Information Interchange, American standard code for information exchange ）

2、 Binary serialization saves more memory space than string representation 【 Integers 、 Representation of numeric values such as floating point numbers 】

We can see , maximal 32 An integer , Namely 2147483647. If it's expressed as an integer , It only needs 32 A bit means . But if you use strings to represent , Altogether 10 Characters , Use... For each character 8 A word of , Need to be whole 80 position . Compared with integer representation , Take up a lot more space .

That's why , A lot of times when we store data , It's binary serialization , Rather than simply passing data through CSV perhaps JSON, This text format is stored for serialization . Whether it's an integer or something , Floating point numbers are good , Using binary serialization will save a lot of space than storing text .

3、 introduce Unicode Character set

ASCII The code just means 128 Characters , It's enough at first . But as more and more people in different countries use computers , I want to express words like Chinese ,128 There are obviously not enough characters . therefore , Computer engineers began to show their own magic , Create a corresponding... For your country's language Character set （Charset） and Character encoding （Character Encoding）.

Character set 【 A collection 】, It can represent a set of characters . such as “ chinese ” It's a character set , But it's not accurate to describe a character set like this . Want to be more precise , We can say ,“ The first edition 《 Xinhua dictionary 》 All the Chinese characters in it ”, This is a character set . such , We can know for sure , A character is not in this set . such as , What we say every day Unicode, It's actually a character set , Contains 150 Language 14 Ten thousand different characters .

Character encoding 【 A set of conversion rules 】, It is For these characters in the character set , How to 11 a dictionary expressed in binary . What we said above Unicode, You can use it UTF-8、UTF-16, Even UTF-32 To code , Store as binary . therefore , With Unicode, In fact, we can use more than UTF-8 A form of coding , We can also invent our own GT-32 code , For example, it's called Geek Time 32 Okay . As long as others know the coding rules , It can be transmitted normally 、 Show this code .
4、“ Hold two Kunjin handcuffs , I cried out in my mouth ” Why ？【 The code problem 】

The essence of garbled code ： The encoding and decoding are inconsistent

summary 【 Key points of personal summary 】

• Original code One of the most intuitive drawbacks of notation is ,0 It can be expressed in two different codes ,1000 representative 0, 0000 On behalf of 0.

• use Complement code To represent negative numbers , Make it easy to add our integers , There's no need to do anything special , Just add it as a normal binary , You can get the right results .

• Practical application of complement ： Binary to decimal 【 Binary is negative 】; Decimal negative to binary 【 Add... In reverse 1】

• Inverse code It is usually used to find the complement from the original code or the transition code from the complement to the original code .

  • When the inverse code is positive with the original code , equally （0001 The opposite of 0001）; When negative , The inverse code is the original code, except for the sign bit , Other bits are reversed .（1001 The opposite of 1110）

• What we say every day Unicode, It's actually a character set , Contains 150 Language 14 Ten thousand different characters .

• Character set （Charset）： A character aggregate .

• Character encoding （Character Encoding）： A set of Characters and numbers Of Conversion or correspondence The rules .

• Character encoding is for these characters in the character set , How to 11 a dictionary expressed in binary . What we said above Unicode, You can use it UTF-8、UTF-16, Even UTF-32 To code , Store as binary .

• The problem of garbled code is actually The encoding and decoding are inconsistent The problem of

【 The principle of computer organization 】 Learning notes —— General catalogue