For any positive integer $n$, let $G(n)$ be the number of pairs of adjacent bits in the binary representation of $n$ which are different. For example, $G(10)=3$ because the bits of $1010_2$ change at all three places and $G(12)=1$ because the bits of $1100_2$ change only from the fours to the twos place. For how many positive integers $n<2^{10}$ is it true that $G(n)=2$?