Sure! Here's a **full solution** for your question based on the grammar of arithmetic expressions with addition and multiplication.
---
### 📘 **Given Grammar:**
```
E → E + T
E → T
T → T * F
T → F
F → digit
```
---
## ✅ (a) Synthesized Attributes and Semantic Rules
We define a **synthesized attribute** `val` to represent the **numeric value** of each non-terminal. The `digit.lexval` holds the integer value of the digit token.
### 🎯 Semantic Rules:
```
E → E1 + T { E.val = E1.val + T.val }
E → T { E.val = T.val }
T → T1 * F { T.val = T1.val * F.val }
T → F { T.val = F.val }
F → digit { F.val = digit.lexval }
```
---
## ✅ (b) Evaluate Expression: `2 + 3 * 4`
### 🔹 Operator Precedence
- According to grammar:
- `*` has **higher precedence** than `+`
- So: `2 + (3 * 4) = 2 + 12 = 14`
---
### 🔢 Step-by-step Attribute Evaluation:
1. `digit(2)` → `F.val = 2` → `T.val = 2` → `E1.val = 2`
2. `digit(3)` → `F.val = 3`
3. `digit(4)` → `F.val = 4` → `T1.val = 3`, `F.val = 4` → `T.val = 3 * 4 = 12`
4. `E.val = E1.val + T.val = 2 + 12 = 14`
✅ Final Result: `E.val = 14`
---
## ✅ (c) Annotated Parse Tree (with Synthesized Attributes)
```
E (14)
/ | \
E(2) + T(12)
| |
T(2) T(12)
| |
F(2) T(3) * F(4)
| |
F(3) F(4)
```
### 🔹 Attribute Flow:
| Symbol | Value |
|------------|--------|
| F(2) | 2 |
| T(2) | 2 |
| E1 | 2 |
| F(3) | 3 |
| F(4) | 4 |
| T(3 * 4) | 12 |
| E(2 + 12) | 14 |
---
Let me know if you’d like this in **PowerPoint** or **PDF** format or want a **tree diagram image** of the parse tree!