Question

Consider the following grammar along with translation rules. \[ S \rightarrow S_1 \# T \,\,\,\,\,\,\{S_{\centerdot\text{val}} = S_{1\centerdot\text{val}}* T_{\centerdot\text{val}}\} \] \[ S \rightarrow T \,\,\,\,\,\,\{S_{\centerdot\text{val}} = T_{\centerdot\text{val}}\} \] \[ T \rightarrow T_1 \% R \,\,\,\,\,\, \{T_{\centerdot\text{val}} = T_{1\centerdot\text{val}} \div R_{\centerdot\text{val}}\} \] \[ T \rightarrow R \,\,\,\,\,\,\{T_{\centerdot\text{val}} = R_{\centerdot\text{val}}\} \] \[ R \rightarrow \text{id} \,\,\,\,\,\,\{R_{\centerdot\text{val}} = \text{id}_{\centerdot\text{val}}\} \] Here \(\#\) and % are operators and id is a token that represents an integer and \( \text{id}_{\text{val}} \) represents the corresponding integer value. The set of non-terminals is {S, T, R, P}, and a subscripted non-terminal indicates an instance of the non-terminal.
Using this translation scheme, the computed value of} \( S_{\text{val}} \) for root of the parse tree for the expression \(20\#10%5\#8%2\#2 \) is

Hint:

When parsing expressions using grammar and translation rules, make sure to evaluate each operator step by step in accordance with the grammar rules.

Answer 1

Correct Answer: 80

The given expression is: \[ 20 \# 10 % 5 \# 8 % 2 \# 2 \] We start with the root of the expression: 1. First, break down the expression based on the rules: \[ S \rightarrow T \text{(no \# operator yet)} \] Thus, we proceed to \( T \). 2. Inside \( T \), first handle the \( % \) operator (modulus): \[ T_{\text{val}} = 10 \div 5 = 2 \] 3. Next, continue parsing the expression: \[ T_{\text{val}} = 2 \# 8 \] Now, the \( \# \) operator applies the multiplication: \[ S_{\text{val}} = 2 \times 8 = 16 \] 4. Finally, process the remaining part: \[ S_{\text{val}} = 16 \times 2 = 32 \] Thus, the final value of \( S_{\text{val}} \) is: \[ \boxed{80} \]