Introduction of C language base conversion and original complement inverse code point operation

Reason for using base

1. Because of the present CPU Only high and low levels can be recognized , Only binary data can be calculated
2. Although binary data can be directly CPU Identify calculations , But it is not convenient to write and record , Because converting binary data into octal is to facilitate recording in documents
3. because CPU The number of digits is increasing , from 8 Bit gradually developed to the present 64 position , Therefore, octal cannot meet the demand gradually , So we developed hexadecimal , However, due to historical reasons, octal cannot be completely eliminated

Hexadecimal conversion

1. Decimal to binary

1. Remainder method ： use 2 Balance the data , Then continue to seek surplus from the business , Until Shang Wei 0 end , The remainder generated in this process is the binary of the data ( The reverse )
   n%2==1\0
   merchant %2 ==1\0
   …
   Until Shang Wei 0
   The reverse order of the remainder is n Binary system

2. Right seeking method ： From high to low , data -2^(n-1) If it's enough , So the first n Bit is 1, Otherwise, it would be 0, Until the data is reduced to 0
   128 64 32 16 8 4 2 1
   86(01010110)
   72(01001000)
   112(01110000)
   176(10110000)

2. Binary to decimal

Everyone's 2^(n-1) Sum up
10010010 145

3. Binary to octal

Starting from the low , Every three binary bits corresponds to one octal
Binary system ： 1 001 010 101 110
octal ： 1 1 2 5 6

4. Binary to hexadecimal

Starting from the low , Every four binary bits corresponds to one hexadecimal
Binary system ： 1 0010 1010 1110
Hexadecimal 1 2 A E
stay C In language , With 0 The first number is octal number 0x The first number is hexadecimal

 		    %c 072
            %o  Display data in octal 
            %x  Display data in hexadecimal 
            %#o %#x  Display the prefix corresponding to the data 

Original code 、 Inverse code 、 Complement code

Original code

Binary of data

Inverse code

 Sign bit 1 It's a negative number 0 Positive number 
 The inverse code of a positive number is its original code 
 The inverse code of a negative number is its original code except for the sign bit , Other bits are inversed bit by bit       

Complement code

The complement of a positive number is its original code
The complement of a negative number is its inverse +1
Be careful ： All data in memory is stored in the form of complement
1、 Negative numbers are converted to binary
2、 The sign bits remain the same , The rest are inversed by position
3、 Inverse code +1 Get the complement
-127
Original code ：1111 1111
Inverse code ：1000 0000
Complement code ：1000 0001

Complement to data

Unsigned complement is directly converted to decimal
The highest sign is 0, The description is positive , It is also directly converted to decimal
Signed and the highest bit is 1：
1、 Complement code -1 Get the inverse
2、 The sign bits remain the same , Other bits are inversed bit by bit to get the original code
3、 Convert the original code into decimal data
1111 1111 Complement code A signed
1111 1110 Inverse code
1000 0001 Original code
-1 Decimal system

Introduction to bitwise operators

A & B Press phase and There are false and false
00110010
11001010
--------
00000010 0x2

A | B Press phase or True and true
00110010
11001010
--------
11111010

~A Reverse by position
00110010
11001101

A ^ B Bitwise XOR Same as 0, Dissimilarity is 1
00110010 0x32
11001101 0xCA
--------
11111000 0xf8

A<<n hold A The complement of moves left n position , Discard the left and fill the right 0
0x32 << 3
00110010 0X32
10010000 0x90

A>>n hold A To the right n position , On the right side of the discarded , Fill in the sign on the left ( Not sign bit complement 0, It is a sign complement 1)
00110010 0X32
11110110

practice ： Enter an integer , It's 4~7 Bit is set to 1010, Other bits cannot be changed

101101011 0111 0101   num
101101011 1010 0101   (num & ~(oxf<4)) | (0xA<<4)
000000000 1010 0000   0xA<<4
101101011 0000 0101   num & ~(oxf<4)
111111111 0000 1111   ~(oxf<4)
000000000 1111 0000   oxf<<4
000000000 0000 1111   oxf