The binary representation $x=0 . b_{1} b_{2} b_{3} \ldots$ of a number $x$ between 0 and 1 can be defined as follows. Let $b_{1}=0$ if $x<1 / 2$ and $b_{1}=1 \quad$ if $\quad 1 / 2 \leq x<1 .$ Let $x_{1}=2 x-b_{1} .$ Let $b_{2}=0$ if $x_{1}<1 / 2$ and $b_{2}=1$ if $1 / 2 \leq x<1 .$ Let $x_{2}=2 x_{1}-b_{2} $ and in general $x_{n}=2 x_{n-1}-b_{n} \quad$ and $\quad b_{n-1}=0 \quad$ if $\quad x_{n}<1 / 2$ and $b_{n-1}=1$ if $1 / 2 \leq x_{n}<1 .$ Find the binary expansion of 1$/ 3$ .