Thoroughly understand bit operations -- and (&), not (~), or (|), XOR (^)

Catalog

And &：

The case is as follows ：

Rules are as follows ：

Practical cases ：

or |：

The case is as follows ：

Rules are as follows ：

Practical cases ：

Exclusive or ^:

The case is as follows ：

Rules are as follows ：

Practical cases ：

Not ~：

summary ：

---

And &：

2 Binary & operation , Only when 2 The values of all are 1 when , The result is 1. All others are returned 0;

The case is as follows ：

15  & 5 = 5

take 15 and 5 The binary of is displayed separately

 

Because only when 2 Both binary are 1 when , The result is 1, Others are 0, So the result is shown in the figure below .

 

Rules are as follows ：

" Binary truncation ", Why binary truncation , Let's use the above example ,15 The binary of is low 4 All places are 1, and 5 The binary of is 0101. because & Operations must all be 1 The result is 1, So can we understand it as 5 hold 15 Other bits of 1 Cut it into 0 What about it ？ Then take another example ,0xFFFF = 65535 = 1111 1111 1111 1111, We use it 0x1 = 1 = 0000 0000 0000 0001 Let's do one & operation . So the result is 1, That is the 0xFFFF The height of 31 All the bits are set as 0, So it's just using 0x1 hold 0xFFFF The height of 31 Bits are truncated to 0.

Practical cases ：

1. So in some low-level operations , For space and time efficiency , It's all used bit Bits are used as identification bits to represent some states , Or address space . So be a 32 The value of bits may contain the address space , There are many status identification bits . When we need to position one of the States as 0 When , We can go through & The operation of . If the second is higher 17 The position is 0, We can use 1111 1111 1111 1111 0111 1111 1111 1111 & Source operands , You can cut off the highest 17 position .
2. The operation of taking remainder ： I still remember when I first started as a programmer , Will do questions to practice , For example, traversal 1-100, Even numbers output something , Odd number output . In fact, it is %2 An operation of remainder . In fact, you can also use & And operation to complete . We find the law , When a decimal system is converted to binary , The last bit of binary is 0, Or 0 Either it's 2 Multiple （ even numbers ）, Instead, if the last one is 1, So either 1, Or it's odd （ Of course 1 It's also odd ）. So the rule is ： Source operands & 1, If 0 Then it's even , If 1 It's an odd number . And the remainder of any number can , When we need to take 1024 The remainder of , We just need to use the source operand & 1024-1, The result is 1024 The remainder of , because 1023 add 1 Is all carry , therefore 1023 yes 1024 All low bits of bit are 1, So pass & Operation can be obtained 1024 The remainder of （ Here the author , Description ability is a little poor , You can test and demonstrate by yourself ）

or |：

2 Binary | operation , It only needs 2 There is one binary 1, The result is 1（2 Both binary are 1 It's also 1）, Well understood. , except 2 Both binary are 0, The other results are 1.

The case is as follows ：

10 | 5 = 15

take 10 and 5 The binary of is displayed separately

Because only 2 There is one binary 1 The results for 1, therefore | After operation, it is shown in the following figure .

Rules are as follows ：

" Binary combination ", It's easy to understand , Don't explain too much , That is the 2 Group binary aligned and combined ....

Practical cases ：

1. As described above & The first practical case in operation , It's about how to use & Operate a bit The status position of bit is 0, that | Whether the operation can place a bit at 1 Well ？ After all, it is binary combination , We just need to write a set of binaries aligned with the source operand , Set the status bit to 1 Which one of them wrote 1, It's done .
2. The first 2 This case is also based on the first case , We see Linux2.6 In the source code of the kernel （ This is a fork and clone when , Configuration items of parent-child processes , I don't know or affect this case ）. We are in the project , Are there many configuration items , Finally, how to manage these configuration items gracefully and efficiently ？ Yes, each configuration corresponds to a set of binaries （ Although the picture is 16 Base number , Just make a decimal conversion ）, Finally through | Operations combine these configurations . When judging whether configuration items can be used & Operation? （ by 0 It means that some configuration items are not enabled , nudges , But in detail ）？

 

Exclusive or ^:

2 It's binary ^ Exclusive or operation , as long as 2 The same result of binary is 0, The difference is 1.（ Note that here is to judge whether it is the same , I didn't judge whether it was again 1）

The case is as follows ：

 

Rules are as follows ：

" Binary carry free addition ", It's easy to understand ,^ The XOR operation is the same as 0, The difference is 1. The same result is 11 perhaps 00, and 11 As the result of the 0,11 So it can be understood that binary adds but does not carry （ Added as 0, But go high 1 Of , But not carry ）, and 00 The sum is still 0. And for the different only 10 perhaps 01. and 01 perhaps 10 The result of XOR operation is 1, And they add up for 1. So it can be explained that XOR is binary non carry addition .

Practical cases ：

1. Disturbance function （ Baidu can understand by itself ）
2. Two number exchange , Use ^ Exclusive or operation , You can not borrow temporary variables .

   a = 0011 0010;
   b = 0010 1010;
   
   a = a ^ b;   //  After operation a = 0001 1000   b = 0010 1010
   b = b ^ a;   //  After operation b = 0011 0010 , a = 0001 1000
   a = a ^ b;   //  After operation a = 0010 1010 , b = 0011 0010

3. 2 Equal numbers ^ Whether the result of XOR operation is 0, So it can be used to judge whether it is equal .

Not ~：

Reverse the whole binary ,0 become 1,1 become 0. This is too easy , Don't draw pictures to understand .

summary ：

After finding the law , You can see the answer at a glance .

Last , If this post is helpful to you , Hope you can praise it + Focus on + Collection ！ Your support is my greatest motivation , The use of various frameworks and the source code interpretation of the framework will be updated all the time ~！