[secsha concept] original reverse supplement

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Positive numbers

negative

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Positive numbers

A positive number 、 back 、 The complement is the same

negative

Original code

Directly translate numbers into binary in the form of positive and negative numbers

Inverse code

Change the sign bit of the original code , The other bits can be inverted in turn

Complement code

Inverse code +1 You get the complement

For plastic surgery ： The form of data in memory is actually complement

In computer system , Integer type value Always use complement to represent and store

Because subtraction can be achieved by adding complements , therefore CPU There is no need to implement a subtracter , Reduced hardware costs  

and The complement of the complement is the original code , therefore CPU You only need to implement the complement and adder to realize the addition, subtraction, multiplication and division of integers

Multiplication is adding more times , Division is to subtract several times , When you want to output a negative number, turn the complement in memory into the source code and then output

Subtraction example ：

1 - 1 = 1 + (-1)

because int The size of the type is 8 Bytes ,1 Bytes 8 A bit , So there is 32 A bit  

1 ：

1 The source code of is

0000 0000 0000 0000 0000 0000 0000 0001

1 The inverse of is

0000 0000 0000 0000 0000 0000 0000 0001

1 The complement of is

0000 0000 0000 0000 0000 0000 0000 0001

-1：

-1 The source code of is  

1000 0000 0000 0000 0000 0000 0000 0001

-1 The inverse of is

1111  1111  1111  1111  1111  1111  1111  1110

-1 The complement of is

1111  1111  1111  1111  1111  1111  1111  1111

Complement addition equals

(1) 0000 0000 0000 0000 0000 0000 0000 0000

In the front brackets 1 Beyond the 4 Bytes 32 A bit , So it was lost , therefore 1 + (-1) As the result of the  0