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masha68 [24]
3 years ago
13

A palindrome is a string whose reversal is identical to the string. How many bit strings of length n are palindromes?

Mathematics
1 answer:
alisha [4.7K]3 years ago
4 0

Answer:

The number of  palindromes is  

      2^{\frac{n}{2} } when n is even and

      2^{\frac{n +1}{2}  } when n is odd

Step-by-step explanation:

From the question we are told that

    The  length of the string is  n

Generally palindrome is evaluated by considering the first part of a string

  When the the length of the string is an even number then

it means that the first part of the string is \frac{n}{2}

Hence the number of  bit strings of length n that are  palindromes is evaluated as

       p(n_{even }) =  2^{\frac{n}{2} }

But When the the length of the string is an odd number then

it means that the first part of the string is \frac{n-1}{2}

Hence the number of  bit strings of length n that are  palindromes is evaluated as

       p(n_{odd }) =2^{\frac{n -1}{2} +1 } = 2^{\frac{n +1}{2}  }

Generally each bit could be either 0 or  1

Hence the number of  palindromes is  

      2^{\frac{n}{2} } when n is even and

      2^{\frac{n +1}{2}  }  when n is odd

           

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