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#FI→I1BI→BF→BF1F→BB→0B→1N.val=I.val+F.valI.val=(2I1.val)+B.valI.val=B.valF.val=21(B.val+F1.val)F.val=21B.valB.val=0.valB.val=1.val
The value computed by the translation scheme for the input string
10#011
is __________. (Rounded off to three decimal places)