Question:
What is the postfix form of the infix expression A + B * C − D / E?
What is the postfix form of the infix expression A + B * C − D / E?
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Handle * and / before + and −. Convert B*C and D/E first, then combine the additive operators left to right.
Updated On: Jul 2, 2026
- A B + C * D E / −
- A B + * C D − /
- A B C D E + * − /
- A B C * + D E / −
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The Correct Option is D
Solution and Explanation
Step 1: Fix precedence. Multiplication and division bind tighter than addition and subtraction, and they associate left to right.
Step 2: Convert the high-precedence parts first. \(B * C\) becomes \(B\,C\,*\). \(D / E\) becomes \(D\,E\,/\).
Step 3: Rewrite the expression using these blocks: \(A + (B\,C\,*) - (D\,E\,/)\).
Step 4: Apply the two additive operators left to right. First \(A + (B\,C\,*)\) becomes \(A\,B\,C\,*\,+\).
Step 5: Then subtract \(D\,E\,/\): take the result so far and append the operand and the minus, giving \(A\,B\,C\,*\,+\,D\,E\,/\,-\).
Step 6: The postfix form is A B C * + D E / −. The correct option is (D).
Step 2: Convert the high-precedence parts first. \(B * C\) becomes \(B\,C\,*\). \(D / E\) becomes \(D\,E\,/\).
Step 3: Rewrite the expression using these blocks: \(A + (B\,C\,*) - (D\,E\,/)\).
Step 4: Apply the two additive operators left to right. First \(A + (B\,C\,*)\) becomes \(A\,B\,C\,*\,+\).
Step 5: Then subtract \(D\,E\,/\): take the result so far and append the operand and the minus, giving \(A\,B\,C\,*\,+\,D\,E\,/\,-\).
Step 6: The postfix form is A B C * + D E / −. The correct option is (D).
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