GATE CS 2023 Set 1 — Question 60
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Compiler Design → Semantic Analysis → Syntax-Directed Translation
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Question
Consider the syntax directed translation given by the following grammar and semantic rules. Here and are non-terminals. is the starting non-terminal, and and are lexical tokens corresponding to input letters "#", "0" and "1", respectively. denotes the synthesized attribute (a numeric value) associated with a non-terminal . and denote occurrences of and on the right hand side of a production, respectively. For the tokens and , and .
The value computed by the translation scheme for the input stringis _______. (Rounded off to three decimal places)
Correct answer
2.374 to 2.376
Solution
The input string is . The grammar splits this into an integer part (before ) and a fractional part (after ).1. Evaluating the Integer Part () for string "10":
The production rules for are:
The production rules for are:
.The value rounded to three decimal places is .
The production rules for are:
- The derivation is .
- First, reduce to : .
- Reduce this to : .
- Next, reduce to : .
- Finally, reduce to : .
The production rules for are:
- The derivation is .
- We evaluate from right to left (bottom-up recursion):
- Last digit : .
- Middle digit : .
- First digit : .
.The value rounded to three decimal places is .
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