ITPEC FE Subject A October 2024 Question 2
What is the value of the postfix expression below? Here, A, B, C, and D are operands whose values are 4, 3, 5, and 6, respectively. Symbols “+”, “−”, “×”, and “÷” are arithmetic operators for addition, subtraction, multiplication, and division, respectively.
A B 2 × + D B ÷ C × −
Explanation
0 — evaluate the postfix expression with a stack, applying each operator to the two values on top.
Substitute A = 4, B = 3, C = 5, D = 6 and scan left to right:
- •push 4, 3, 2; apply × → 3 × 2 = 6, stack 4, 6
- •apply + → 4 + 6 = 10, stack 10
- •push 6, 3; apply ÷ → 6 ÷ 3 = 2, stack 10, 2
- •push 5; apply × → 2 × 5 = 10, stack 10, 10
- •apply − → 10 − 10 = 0
In infix form this is (A + B × 2) − (D ÷ B × C) = 10 − 10 = 0.
Answer (b)
Why not others:
- •(a) −3 and (c) 3 — both halves of the final subtraction equal 10, so a correct evaluation can only give 0; a nonzero result means an operator was applied to the wrong operands
- •(d) 40/3 — the only division is 6 ÷ 3 = 2, which is exact, so no fraction can appear in a correct evaluation
Key rule: In postfix, an operator takes the two values on top of the stack and the value popped second is the left operand, which matters for − and ÷.
Basic Theory · AI-written, may contain errors
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