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-ter

Question

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 #, 0 and 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. I1 and F1 denote occurrences of I and F on the right hand side of a production, respectively. For the tokens 0 and 1, 0.val = 0 and 1.val = 1.
N → I # F     { N.val = I.val + F.val }
I → I1 B      { I.val = (2 * I1.val) + B.val }
I → B         { I.val = B.val }
F → B F1      { F.val = (1/2) * (B.val + F1.val) }
F → B         { F.val = (1/2) * B.val }
B → 0         { B.val = 0.val }
B → 1         { B.val = 1.val }
The value computed by the translation scheme for the input string 10#011 is __________. (Rounded off to three decimal places)

Accepted Answer

2.375

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