Q50

Consider the syntax directed translation given by the following grammar and semantic rules. Here $N, I, F$ and $B$ are non-terminals. $N$ is the starting non-terminal, and $\#, \mathbf{0}$ and $\mathbf{1}$ are lexical tokens corresponding to input letters \text{“#", “0" and “1"}, respectively. $X.val$ denotes the synthesized attribute (a numeric value) associated with a non-terminal $X. \;I_{1}$ and $F_{1}$ denote occurrences of $I$ and $F$ on the right hand side of a production, respectively. For the tokens $\mathbf{0}$ and $\mathbf{1}, \mathbf{0} . v a l=0$ and $\mathbf{1}.val =1$.

$$\begin{array}{ll} N \rightarrow I \# F & N.val =I . v a l+F . v a l \\ I\rightarrow I_{1} B & I.val =\left(2 I_{1} . v a l\right)+B.val \\ I \rightarrow B & I.val =\text { B.val } \\ F \rightarrow B F_{1} & F.val =\frac{1}{2}\left(B . v a l+F_{1} . v a l\right) \\ F \rightarrow B & \text { F.val }=\frac{1}{2} B.val \\ B \rightarrow \mathbf{0} & B . v a l=\mathbf{0} . v a l \\ B \rightarrow \mathbf{1} & B . v a l=\mathbf{1} . v a l \\ \end{array}$$

The value computed by the translation scheme for the input string

$$10\#011$$

is ____________. (Rounded off to three decimal places)