C Primer Plus Chapter 15 (bit operation)

1. Binary system 、 Bits and bytes

• With 2 The number represented by the base is called Binary number （binary number）

1		  1		 	0		  1
1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 13

1.1 Binary integer

• C Language use byte （byte） Represents the required size of the storage system character set

  • 1 byte = 8 position

• Yes 1 byte （8 position ） In different ways Bit combination （bit pattern）

  • unsigned char: 0000 0000 ~ 1111 1111 = 0 ~ 255

  • signed char : 1000 0000 ~ 0111 1111 = -128 ~ 127

1.2 Signed integers

• Sign quantity （sign-magnitude） notation ：1 position ** Higher order potential （high-order bit）** Store symbols , be left over 7 Bits represent the number itself

  • 1111 1111 ~ 0111 1111 = -127 ~ 127
  • There are two 0 ：
    • 0000 0000 = +0
    • 1000 0000 = -0

• Binary complement （two’s-complement） Method ： Take the opposite , Add 1

  • 1111 1111 ~ 0111 1111 = -128 ~ 127

• Binary inverse （one’s-complement） Method ： Take the opposite

  • 1000 0000 ~ 0111 1111 = -127 ~ 127
  • There are two 0 ：
    • 0000 0000 = +0
    • 1111 1111 = -0

1.3 Binary floating point numbers

• Floating point numbers are stored in two parts
  • Binary decimals
  • Binary index

1.3.1 Binary decimals

• With 2 Power of as denominator

1	  0		1
1/2 + 0/4 + 1/8 = 0.625

• Many fractions cannot be accurately represented by binary decimals
  • It can only accurately represent multiple 1/2 The sum of the powers of

1.3.2 floating-point number

• Several bits store binary fractions , Other bits store index

2. Other hexadecimal numbers

• Octal and hexadecimal numeration systems are usually used

2.1 octal

• octal （octal） It refers to octal numeration system
• With 8 Represent numbers for the base

4		  5			1
4 * 8^2 + 5 * 8^1 + 1 * 8^0 = 297

• Each octal digit corresponds to 3 Binary bits

  • Binary equivalent to octal

    Octal digit	Equivalent binary
    0	000
    1	001
    2	010
    3	011
    4	100
    5	101
    6	110
    7	111

2.2 Hexadecimal

• Hexadecimal （hexadecimal or hex） It refers to the hexadecimal numeration system
• With 16 Represent numbers for the base

A			3			F
10 * 16^2 + 3 * 16^1 + 15 * 16^0 = 2623

• Each hexadecimal digit corresponds to 4 Binary bits

  • Decimal system 、 Hexadecimal and equivalent binary digits

    Decimal system	Hexadecimal	Equivalent binary
    0	0	0000
    1	1	0001
    2	2	0010
    3	3	0011
    4	4	0100
    5	5	0101
    6	6	0110
    7	7	0111
    8	8	1000
    9	9	1001
    10	A	1010
    11	B	1011
    12	C	1100
    13	D	1101
    14	E	1110
    15	F	1111

3. C Bitwise operators

3.1 Bitwise logical operators

• Bitwise （bitwise） operation ： Operations are carried out for each bit , It doesn't affect the left and right bits

3.1.1 Binary inversion or bitwise inversion ：~

• hold 1 Turn into 0 , hold 0 Turn into 1
• The operator does not change the original value

char c = 0b10011010;
~c;
printf("%d\n%d\n", c, ~c);
// ~(1001 1010) = -102
// 0110 0101 = 101

3.1.2 Bitwise AND ：&

• A fellow 1 Only then 1

char c1 = 0b10010011;
char c2 = 0b00111101;
printf("%d\n", c1 & c2);
// 1001 0011
// 0011 1101
// &
// 0001 0001

3.1.3 Press bit or ：|

• Yes 1 Then for 1

char c1 = 0b10010011;
char c2 = 0b00111101;
printf("%d\n", c1 | c2);
// 1001 0011
// 0011 1101
// |
// 1011 1111

3.1.4 Bitwise XOR ：^

• The difference is 1

char c1 = 0b10010011;
char c2 = 0b00111101;
printf("%d\n", c1 ^ c2);
// 1001 0011
// 0011 1101
// ^
// 1010 1110

3.7 Shift Operators

3.7.1 Move left ：<<

• Move the object to the left of the operator to the left , The number of bits specified by the right object
• The operator does not change the original value

char c = 0b10001010;
c << 2;
printf("%d\n%d\n", c, c << 2);
// 00 1000 1010
// 10 0010 1000
//  High truncation 
// 0010 1000

3.7.2 Move right ：>>

• Move the object to the left of the operator to the right , The number of bits specified by the right object
• The operator does not change the original value

char c = 0b10001010;
c >> 2;
printf("%d\n%d\n", c, c >> 2);
// 1000 1010
// 1110 0010 10
//  Low truncation 
// 1110 0010

3.7.3 usage ： Shift Operators

• in the light of 2 The power of provides fast multiplication and division
  • number << n ：number multiply 2 Of n The next power
  • number >> n ： If number non-negative , Then use number Divide 2 Of n The next power

4. Bit fields

• Bit fields （bit field） It's a signed int or unsigned int A set of adjacent bits in a type variable
• Build through a structure declaration

struct {
    
    int a : 1;
    int b : 2;
    int c : 3;
} abc;
// abc  Include for  3  individual  1  Bit field 

abc.a = 0;
abc.c = 1;
//  Because the number of digits in the field is  1 , So it can only be assigned  0  or  1

• If the total number of digits declared exceeds int （unsigned int Empathy ） Number of digits , Will use the next one int Storage location

  • When this happens , first int Will leave an unnamed “ hole ”
  • You can use unnamed field widths “ fill ” Unnamed “ hole ”
  • Use a width of 0 The unnamed field of causes the next field to be stored in the next int in

  struct {
        
      int a : 1;
      int   : 2;
      int b : 2;
      int   : 0;
      int c : 3;
  } abc;
  // a  and  b  There is a  2  Bit gap 
  // c  Will be stored in the next  int z