Discrete mathSolutiona a binary word is a combination of 0s

Discrete math

Solution

a> a binary word is a combination of 0\'s and 1\'s.

FOr this problem the words would always have a length greater than 1 , that is no 0 length word.

Let An be the number of strings of length n that end in a 1, and have no two consecutive zeros.

Let Bn be the number of strings of length n that end in a 0, and have no two consecutive zeros

THus A1 = 1 , B1 = 1

A2 = 2 , {words 01 ,11}

B2 = 1 {word 10}

Number of binary words with no consecutive zeros = Number of words with no consecutive zeros and

ends in 1 + Number of words with no consecutive zeros and ends in 0.

Hence , Number of binary words with no consecutive zeros = An + Bn = Fn + F(n+1) = F(n+2)