GATE CSE 2023 Q60: Value of 10#011 under a binary-fraction translation scheme

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 “#”, “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 $\mathbf{1}$, $\mathbf{0}.val = 0$ and $\mathbf{1}.val = 1$.

$$\begin{array}{lll} N \to I \,\#\, F & & N.val = I.val + F.val \\ I \to I_1\, B & & I.val = (2\, I_1.val) + B.val \\ I \to B & & I.val = B.val \\ F \to B\, F_1 & & F.val = \frac{1}{2}(B.val + F_1.val) \\ F \to B & & F.val = \frac{1}{2} B.val \\ B \to \mathbf{0} & & B.val = \mathbf{0}.val \\ B \to \mathbf{1} & & B.val = \mathbf{1}.val \end{array}$$

The value computed by the translation scheme for the input string

$$10\#011$$

is _______. (Rounded off to three decimal places)