给定整数N。任务是编写程序以查找给定数字的奇偶校验。
注意:数字奇偶校验用于定义数字中的置位总数(二进制表示形式为1位)是偶数还是奇数。如果一个数字的二进制表示形式中的置位总数为偶数,则该数字被称为具有偶数奇偶校验,否则,它将具有奇数奇偶校验。
例子:
Input : N = 13
Output : Odd Parity
Explanation:
Binary representation of 13 is (1101)
Input : N = 9 (1001)
Output : Even Parity
通过执行以下操作,可以有效地计算由32位表示的数字的奇偶校验。
假设给定数字为x,然后执行以下操作:
- y = x ^(x >> 1)
- y = y ^(y >> 2)
- y = y ^(y >> 4)
- y = y ^(y >> 8)
- y = y ^(y >> 16)
现在,y中最右边的位将表示x的奇偶校验。如果最右边的位是1,则x将具有奇数奇偶校验,如果它是0,则x将具有偶数奇偶校验。
因此,为了提取y的最后一位,请对y与1进行按位与运算。
为什么这样做?
Consider that we want to find the parity of n = 150 = 1001 0110 (in binary).
1. Let’s divide this number into two parts and xor them and assign it to n: n = n ^ (n >> 4) = 1001 ^ 0110 = 1111.
Dissimilar bits result in a 1 bit in the result while similar bits result in a 0. We have basically considered all 8 bits to arrive at this intermediate result. So, effectively we have nullified even parities within the number.
Now repeat step 1 again until you end up with a single bit.
n = n ^ (n >> 2) = 11 ^ 11 = 00
n = n ^ (n >> 1) = 0 ^ 0 = 0
Final result = n & 1 = 0
Another example:
n = 1000 0101
n = n ^ (n >> 4) = 1000 ^ 0101 = 1101
n = n ^ (n >> 2) = 11 ^ 01 = 10
n = n ^ (n >> 1) = 1 ^ 0 = 1
Final result = n & 1 = 1
if(y&1==1)
odd Parity
else
even Parity
下面是上述方法的实现:
C++
// Program to find the parity of a given number
#include
using namespace std;
// Function to find the parity
bool findParity(int x)
{
int y = x ^ (x >> 1);
y = y ^ (y >> 2);
y = y ^ (y >> 4);
y = y ^ (y >> 8);
y = y ^ (y >> 16);
// Rightmost bit of y holds the parity value
// if (y&1) is 1 then parity is odd else even
if (y & 1)
return 1;
return 0;
}
// Driver code
int main()
{
(findParity(9)==0)?cout<<"Even Parity\n":
cout<<"Odd Parity\n";
(findParity(13)==0)?cout<<"Even Parity\n":
cout<<"Odd Parity\n";
return 0;
}
Java
// Program to find the
// parity of a given number
import java.io.*;
class GFG
{
// Function to find the parity
static boolean findParity(int x)
{
int y = x ^ (x >> 1);
y = y ^ (y >> 2);
y = y ^ (y >> 4);
y = y ^ (y >> 8);
y = y ^ (y >> 16);
// Rightmost bit of y holds
// the parity value
// if (y&1) is 1 then parity
// is odd else even
if ((y & 1) > 0)
return true;
return false;
}
// Driver code
public static void main (String[] args)
{
if((findParity(9) == false))
System.out.println("Even Parity");
else
System.out.println("Odd Parity");
if(findParity(13) == false)
System.out.println("Even Parity");
else
System.out.println("Odd Parity");
}
}
// This Code is Contributed by chandan_jnu.
Python3
# Program to find the
# parity of a given number
# Function to find the parity
def findParity(x):
y = x ^ (x >> 1);
y = y ^ (y >> 2);
y = y ^ (y >> 4);
y = y ^ (y >> 8);
y = y ^ (y >> 16);
# Rightmost bit of y holds
# the parity value if (y&1)
# is 1 then parity is odd
# else even
if (y & 1):
return 1;
return 0;
# Driver code
if(findParity(9) == 0):
print("Even Parity");
else:
print("Odd Parity\n");
if(findParity(13) == 0):
print("Even Parity");
else:
print("Odd Parity");
# This code is contributed by mits
C#
// Program to find the
// parity of a given number
using System;
class GFG
{
// Function to find the parity
static bool findParity(int x)
{
int y = x ^ (x >> 1);
y = y ^ (y >> 2);
y = y ^ (y >> 4);
y = y ^ (y >> 8);
y = y ^ (y >> 16);
// Rightmost bit of y holds
// the parity value
// if (y&1) is 1 then parity
// is odd else even
if ((y & 1) > 0)
return true;
return false;
}
// Driver code
public static void Main ()
{
if((findParity(9) == false))
Console.WriteLine("Even Parity");
else
Console.WriteLine("Odd Parity");
if(findParity(13) == false)
Console.WriteLine("Even Parity");
else
Console.WriteLine("Odd Parity");
}
}
// This Code is Contributed
// by chandan_jnu
PHP
> 1);
$y = $y ^ ($y >> 2);
$y = $y ^ ($y >> 4);
$y = $y ^ ($y >> 8);
$y = $y ^ ($y >> 16);
// Rightmost bit of y holds
// the parity value if (y&1)
// is 1 then parity is odd
// else even
if ($y & 1)
return 1;
return 0;
}
// Driver code
(findParity(9) == 0) ?
print("Even Parity\n"):
print("Odd Parity\n");
(findParity(13) == 0) ?
print("Even Parity\n"):
print("Odd Parity\n");
// This Code is Contributed by mits
?>
Even Parity
Odd Parity
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