This grammar generates binary numbers with an optional negative sign $(-)$ and $$ optional decimal point:$$ S $$ N $/-$ N$$ N $$ L $.$ L $/$ L$$ L $$ L B $/$ B $$ B $0/1$ Design an L$-$attributed definition to compute S$.$val, the decimal number value of the input string.$$ a$)$ For example, the translation of $101\mathrm{.}101$ should be the decimal number $5\mathrm{.}625$ b$)$ Draw parse tree for string $-101\mathrm{.}101$ and annotate the nodes with values computed by the rules. $$