1. Basic concepts
Truth value ：+0101,-0100; Number of machines ： [x] primary =0101
2. Several machines
Original code ：x = -0101,[x] primary = 1101
Inverse code ：x = -0101,[x] back = 1010
Complement code ：x = -0101,[x] repair = 1011
Shift the code ：x = -0101,[x] move = 2^n + x = 0011
PS： Let's talk about our understanding of complement and shift . Complement is to reduce subtraction to add for the convenience of computer design and operation , Code shifting is for the convenience of size comparison , Used in the order code of floating-point numbers .
Complement code —— In any modular system , Subtraction can be expressed by adding its complement . The simplest example is 12 A watch for a model , For example, now it is 3 spot , that -5 Hours Is equal to +7 Hours , All are 10 spot . here 7 Namely 5 Complement .
Shift the code —— Data correspondence moves one position at a time , Make the number that looks small really small . Like the original 0000 Express 0, Now it means -128, then 0001 Express -127, Until 1111 Express +127, This is convenient for comparison .
3. Fixed point number and floating point number
Fixed-point number ： Fixed decimal point x.xxxxxx, Indicates that the scope is limited , Forget it
Floating point numbers ： The range and precision of numbers are expressed respectively .
General format ：EEEE......EMMM.......M,E Part of it is Order code （ The range of numbers i）,M Part of it is mantissa （ The precision of numbers ）. shortcoming ： Order code and mantissa digit are not fixed , Too flexible.
IEEE754 Format ： Come back with me ----
32 It is （ Single precision ）：1 Bit sign bit S + 8 Skewness index E + 23 Bit effective mantissa M, The offset value is 127.
64 It is （ Double precision ）：1 Bit sign bit S + 11 Skewness index E + 52 Bit effective mantissa M, The offset value is 1023.
It's worth it （32 Position as an example ） N = (-1)^S * 2^(E-127) * 1.M
The special case of floating-point numbers ：
E=0,M=0： Machine zero
E=255,M=0： infinity , Corresponding to x/0
E=255,M!=0： Non numerical NaN, Corresponding 0/0
ps： Attach a copy of IEEE754 file ：https://files.cnblogs.com/files/flashsun/7542008-2008.pdf
4. data verification
The basic principle ： Add redundancy code
Yardage ： The minimum number of different binary digits between legal codes
Code spacing and error detection 、 Error correction ability ：
Yardage d>=e+1： Check e A mistake
Yardage d>=2t+1： correct t A mistake
Yardage d>=e+t+1： Check at the same time e A mistake , And correct t A mistake .（e>=t）
PS： Here's my understanding , Increasing the code spacing is to increase the number of illegal codes , It's OK to see illegal code A mistake has been detected , And the illegal code distance which legal code is more advanced thinks what should be right （ Simple understanding , Please refer to the figure below ）, That is, yes Correct mistakes . I've seen a good understanding of geometry here , Savor carefully ：
for instance ： Let's say there are 8 position , The code distance is 1 Then check no mistakes , Because all codes are legal . If the code distance is 2, That legal code should look like 00000000,00000011,00001100,00001111 such , Then if there is 00000001 Such illegal coding is wrong , A dislocation can be checked , But if two people are wrong at the same time , Then it's possible to jump to another legal code , I can't find out 2 Dislocation .
Then if the yard distance is 3, That legal code should look like 00000000,00000111,00111000,00111111 such , So if there's a dislocation 00000001, Or two dislocations 00000011, It's all illegal code , Can check out mistakes , And right now 00000001 by 00000000, correct 00000011 by 00000111. But if three people are wrong at the same time, they can't be checked out .
Common verification strategies ： Parity check ,CRC check , Hemingway check
ps： Hemingway coding the strongest video demonstration course ：https://www.youtube.com/watch?v=373FUw-2U2k
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