Why does the maximum plus one equal the minimum

Sometimes the maximum value is accidentally added in the program1,We will get a negative number,This negative number is the minimum value for this data type.

下面看一个示例：

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       public 
       
       class 
       
       Number {
       
       
  
       
       public 
       
       static 
       
       void 
       
       main(
       
       String[] 
       
       args) {
       
       
    
       
       System.
       
       out.
       
       println(
       
       "最大的整数：" 
       
       + 
       
       Integer.
       
       MAX_VALUE);
       
       
    
       
       System.
       
       out.
       
       println(
       
       "最大的整数（二进制）：" 
       
       + 
       
       Integer.
       
       toBinaryString(
       
       Integer.
       
       MAX_VALUE));
       
       
    
       
       System.
       
       out.
       
       println(
       
       "最小的整数：" 
       
       + 
       
       Integer.
       
       MIN_VALUE);
       
       
    
       
       System.
       
       out.
       
       println(
       
       "最小的整数（二进制）：" 
       
       + 
       
       Integer.
       
       toBinaryString(
       
       Integer.
       
       MIN_VALUE));
       
       
    
       
       System.
       
       out.
       
       println();
       
       
    
       
       long 
       
       num1 
       
       = 
       
       Integer.
       
       MAX_VALUE 
       
       + 
       
       1;
       
       
    
       
       System.
       
       out.
       
       println(
       
       "最大的数" 
       
       + 
       
       Integer.
       
       MAX_VALUE 
       
       + 
       
       "加一等于" 
       
       + 
       
       num1);
       
       
    
       
       long 
       
       num2 
       
       = 
       
       2147483647L 
       
       + 
       
       1;
       
       
    
       
       System.
       
       out.
       
       println(
       
       "Coercive type conversion during operation");
       
       
    
       
       System.
       
       out.
       
       println(
       
       "最大的数" 
       
       + 
       
       Integer.
       
       MAX_VALUE 
       
       + 
       
       "加一等于" 
       
       + 
       
       num2);
       
       
  }
       
       
}
      
      
      
      

       
       
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运行结果：

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       最大的整数：2147483647
       
       

       
       最大的整数（二进制）：1111111111111111111111111111111
       
       

       
       最小的整数：
       
       -
       
       2147483648
       
       

       
       最小的整数（二进制）：10000000000000000000000000000000
       
       

       
       

       
       最大的数2147483647加一等于
       
       -
       
       2147483648
       
       

       
       Coercive type conversion during operation
       
       

       
       最大的数2147483647加一等于2147483648
      
      
      
      

       
       
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从结果可以看出：The largest integer plus one does indeed become the smallest integer,This is more evident from their binary form.When calculating inside the computer, the addition operation is performed in two's complement form.很显然,最大的数01111111111111111111111111111111+1=10000000000000000000000000000000,这里的10000000000000000000000000000000是-2147483648的补码形式.

If we convert the data type into a data type with a larger storage capacity during the operation,There will be no such result that this becomes a negative number.2147483647L + 1是long型的2147483647+1This will not overflow into a negative number.

此外,还需要注意的是在Java和C#中int是32位,long是64位,We have no problem converting this way.但是在C++语言中short、int和longThe number of bits depends on the operating system.我们只能说short<=int<=long,Of course, the two equal signs do not hold at the same time.So sometimes we seelong long这样的写法,long long是比longtype with larger capacity.在VC++中long long也写作_int64.