ITPEC FE Morning October 2023 Question 5

Infix to Postfix Notation — convert 2+5×3+4 respecting operator precedence.

Step-by-step:

• •Original infix: 2 + 5 × 3 + 4
• •With precedence: (2 + (5 × 3)) + 4
• •Convert innermost first: 5 × 3 → 5 3 ×
• •Then 2 + result → 2 5 3 × +
• •Then result + 4 → 2 5 3 × + 4 +

Verification by stack execution of `2 5 3 × + 4 +`:
- Push 2, 5, 3
- ×: pop 5, 3 → push 15
- +: pop 2, 15 → push 17
- Push 4
- +: pop 17, 4 → push 21 ✓

Why not others:
- (a) 2 5 3 4 × + + — evaluates to 2+(5+(3×4)) = 19
- (b) 2 5 + 3 4 × + — evaluates to (2+5)+(3×4) = 19
- (c) 2 5 3 + × 4 + — evaluates to (2×(5+3))+4 = 20

Key rule: In postfix, higher-precedence operators appear earlier (closer to their operands). Always verify by stack-executing the result.

AI-generated — may contain errors