算法题：如何实现1和2的二进制补码？

本文概述

• 建议：在继续解决方案之前, 请先在"实践"上解决它。
• C ++
• Java
• Python3
• C#

给定二进制数作为字符串, 请打印其1和2的补码。

1的补码二进制数的``0''是通过切换其中的所有位获得的另一个二进制数, 即将0位转换为1, 将1位转换为0。

例子：

1's complement of "0111" is "1000"
1's complement of "1100" is  "0011"

2的补码

二进制数的1被加到二进制数的1的补码上。

例子：

2's complement of "0111" is  "1001"
2's complement of "1100" is  "0100"

推荐：请在"实践首先, 在继续解决方案之前。

作为补充, 我们只需要翻转所有位。

对于2的补语, 我们首先找到一个人的补语。我们从LSB(最低有效位)开始遍历一个补数, 并查找0。我们翻转所有1(更改为0), 直到找到0。最后, 翻转找到的0。例如, 2的补数为" 01000" "是" 11000"(请注意, 我们首先找到01000的补码为10111)。如果全为1(补全), 则在字符串中添加额外的1。例如, 2的补码" 000"为" 1000"(1的补码" 000"为" 111")。

下面是实现。

C ++

// C++ program to print 1's and 2's complement of
// a binary number
#include <bits/stdc++.h>
using namespace std;
  
// Returns '0' for '1' and '1' for '0'
char flip( char c) { return (c == '0' )? '1' : '0' ;}
  
// Print 1's and 2's complement of binary number
// represented by "bin"
void printOneAndTwosComplement(string bin)
{
     int n = bin.length();
     int i;
  
     string ones, twos;
     ones = twos = "" ;
  
     //  for ones complement flip every bit
     for (i = 0; i < n; i++)
         ones += flip(bin[i]);
  
     //  for two's complement go from right to left in
     //  ones complement and if we get 1 make, we make
     //  them 0 and keep going left when we get first
     //  0, make that 1 and go out of loop
     twos = ones;
     for (i = n - 1; i >= 0; i--)
     {
         if (ones[i] == '1' )
             twos[i] = '0' ;
         else
         {
             twos[i] = '1' ;
             break ;
         }
     }
  
     // If No break : all are 1  as in 111  or  11111;
     // in such case, add extra 1 at beginning
     if (i == -1)
         twos = '1' + twos;
  
  
     cout << "1's complement: " << ones << endl;
     cout << "2's complement: " << twos << endl;
}
  
// Driver program
int main()
{
     string bin = "1100" ;
     printOneAndTwosComplement(bin);
     return 0;
}

Java

// Java program to print 1's and 2's complement of
// a binary number
  
class GFG 
{
  
     // Returns '0' for '1' and '1' for '0'
     static char flip( char c)
     {
         return (c == '0' ) ? '1' : '0' ;
     }
  
     // Print 1's and 2's complement of binary number
     // represented by "bin"
     static void printOneAndTwosComplement(String bin)
     {
         int n = bin.length();
         int i;
  
         String ones = "" , twos = "" ;
         ones = twos = "" ;
  
         // for ones complement flip every bit
         for (i = 0 ; i < n; i++)
         {
             ones += flip(bin.charAt(i));
         }
  
         // for two's complement go from right to left in
         // ones complement and if we get 1 make, we make
         // them 0 and keep going left when we get first
         // 0, make that 1 and go out of loop
         twos = ones;
         for (i = n - 1 ; i >= 0 ; i--)
         {
             if (ones.charAt(i) == '1' )
             {
                 twos = twos.substring( 0 , i) + '0' + twos.substring(i + 1 );
             } 
             else
             {
                 twos = twos.substring( 0 , i) + '1' + twos.substring(i + 1 );
                 break ;
             }
         }
  
         // If No break : all are 1 as in 111 or 11111;
         // in such case, add extra 1 at beginning
         if (i == - 1 )
         {
             twos = '1' + twos;
         }
  
         System.out.println( "1's complement: " + ones);;
         System.out.println( "2's complement: " + twos);
     }
  
     // Driver code
     public static void main(String[] args)
     {
         String bin = "1100" ;
         printOneAndTwosComplement(bin);
     }
}
  
// This code contributed by Rajput-Ji

Python3

# Python3 program to print 1's and 2's 
# complement of a binary number 
  
# Returns '0' for '1' and '1' for '0' 
def flip(c):
     return '1' if (c = = '0' ) else '0'
  
# Print 1's and 2's complement of 
# binary number represented by "bin" 
def printOneAndTwosComplement( bin ):
  
     n = len ( bin ) 
     ones = ""
     twos = ""
      
     # for ones complement flip every bit 
     for i in range (n):
         ones + = flip( bin [i]) 
  
     # for two's complement go from right 
     # to left in ones complement and if
     # we get 1 make, we make them 0 and 
     # keep going left when we get first 
     # 0, make that 1 and go out of loop 
     ones = list (ones.strip(""))
     twos = list (ones)
     for i in range (n - 1 , - 1 , - 1 ):
      
         if (ones[i] = = '1' ):
             twos[i] = '0'
         else :         
             twos[i] = '1'
             break
  
     i - = 1    
     # If No break : all are 1 as in 111 or 11111 
     # in such case, add extra 1 at beginning 
     if (i = = - 1 ):
         twos.insert( 0 , '1' ) 
  
     print ( "1's complement: " , * ones, sep = "")
     print ( "2's complement: " , * twos, sep = "")
      
# Driver Code
if __name__ = = '__main__' :
     bin = "1100"
     printOneAndTwosComplement( bin .strip(""))
      
# This code is contributed 
# by SHUBHAMSINGH10

C#

// C# program to print 1's and 2's complement of
// a binary number
using System;
  
class GFG 
{
  
     // Returns '0' for '1' and '1' for '0'
     static char flip( char c)
     {
         return (c == '0' ) ? '1' : '0' ;
     }
  
     // Print 1's and 2's complement of binary number
     // represented by "bin"
     static void printOneAndTwosComplement(String bin)
     {
         int n = bin.Length;
         int i;
  
         String ones = "" , twos = "" ;
         ones = twos = "" ;
  
         // for ones complement flip every bit
         for (i = 0; i < n; i++)
         {
             ones += flip(bin[i]);
         }
  
         // for two's complement go from right to left in
         // ones complement and if we get 1 make, we make
         // them 0 and keep going left when we get first
         // 0, make that 1 and go out of loop
         twos = ones;
         for (i = n - 1; i >= 0; i--)
         {
             if (ones[i] == '1' )
             {
                 twos = twos.Substring(0, i) + '0' + 
                 twos.Substring(i + 1, twos.Length-(i+1));
             } 
             else
             {
                 twos = twos.Substring(0, i) + '1' + 
                 twos.Substring(i + 1, twos.Length-(i+1));
                 break ;
             }
         }
  
         // If No break : all are 1 as in 111 or 11111;
         // in such case, add extra 1 at beginning
         if (i == -1)
         {
             twos = '1' + twos;
         }
  
         Console.WriteLine( "1's complement: " + ones);;
         Console.WriteLine( "2's complement: " + twos);
     }
  
     // Driver code
     public static void Main(String[] args)
     {
         String bin = "1100" ;
         printOneAndTwosComplement(bin);
     }
}
  
// This code has been contributed by 29AjayKumar

输出如下：

1's complement: 0011
2's complement: 0100

谢谢乌特卡什·特里维迪(Utkarsh Trivedi)对于上述解决方案。

另外, 带符号的数字通常使用2的补码表示。正值按原样存储, 负值按2的补码形式存储。需要额外一位来指示数字是正数还是负数。例如, char在C中为8位。如果对char使用2的补码表示形式, 则按原样存储127, 即01111111, 其中第一个0表示正数。但是-127被存储为10000001。

相关文章：

二进制字符串的2补码的有效方法

如果发现任何不正确的地方, 或者想分享有关上述主题的更多信息, 请写评论。

参考文献：

http://qa.lsbin.org/6439/write-program-calculate-ones-and-twos-complement-of-number

http://geeksquiz.com/whats-difference-between-1s-complement-and-2s-complement/