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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