Ullman (Compiler Design) Edition 2 Exercise 5.2 Question 5 (Page No. 317)

Question

This grammar generates binary numbers with a "decimal" point:

• $S\rightarrow L.L\mid L$
• $L\rightarrow LB\mid B$
• $B\rightarrow 0\mid 1$ 

Design an S-attributed SDD to compute $S.val$, the decimal-number value of an input string. For example, the translation of string $101.101$ should be the decimal number $5.625$.

Comments

@Lakshman Patel RJIT

pls remove the hint part from the question as it is not part of it. Also they've asked to design S-attributed SDD so there will be no use of inherited attributes

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@aditi19

Fixed it

Answer 1

$S\rightarrow L.L$	$S.val=L_{1}.val+\frac{L_{2}.val}{2^{L_{2}.count}}$
$S\rightarrow L$	$S.val=L.val$
$L\rightarrow LB$	$L.val=2*L_{1}.val+B.val$ $L.count=L_{1}.count+B.count$
$L\rightarrow B$	$L.val=B.val$ $L.count=B.count$
$B\rightarrow 0$	$B.val=0$ $B.count=1$
$B\rightarrow 1$	$B.val=1$ $B.count=1$