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Free A-Level Computer Science guide
The position of an operator tells a stack evaluator when to combine its operands. Use subtraction and division to check that the first pop is the right operand.
Content owner: Michael Print · Written for A-Level learners · Checked against official specifications
Explore the idea
Read a token, update the operand stack, and predict the next top value. Switch to conversion to move from infix notation to a postfix token stream.
Infix places an operator between operands: (12−3)/2. RPN places each operator after the two expressions it combines: 12 3 − 2 /. Its order encodes grouping, so the evaluator does not need parentheses in the RPN stream.
Push operands. At a binary operator, pop the right operand first, then the left, evaluate left operator right, and push the result. A complete valid expression ends with exactly one value.
AQA 7517 · 4.3.2.1; 4.3.3.1
Useful foundations
By the end, you should be able to
AQA: simple infix↔RPN conversion, expression trees/post-order and stack evaluation. The local conversion model supports binary +, −, × and / with parentheses; it does not claim to parse every programming-language expression.
Shared foundations and optional extensions are labelled separately; this page does not claim complete coverage of the qualification.
For (12−3)/2, the root is division. Its left child is the subtraction subtree with leaves 12 and 3; its right child is 2. Post-order visits left subtree, right subtree, then the parent operator: 12 3 − 2 /.
To rebuild infix from RPN, push operand strings. On an operator, pop right text and left text, then push '(left operator right)'. Fully parenthesising each new expression preserves grouping even when the original used fewer brackets.
Operands go straight to the output. Hold operators on a separate operator stack. Before pushing a new left-associative operator, emit operators already on top with greater or equal precedence. An opening parenthesis is a boundary; a closing one emits up to that boundary.
For 2+3×4, output 2 3 4 × +: multiplication combines 3 and 4 before addition. For 8/2/2, equal-precedence left association gives 8 2 / 2 /, which evaluates to 2. Reordering it as 8 2 2 / / gives 8 instead.
With stack [12,3], subtraction pops 3 as right and 12 as left, then pushes 9. Reading 2 makes [9,2]; division produces 4.5. The illustration uses real-number division, not integer quotient; follow a question's operator definitions.
An operator with fewer than two operands cannot execute. Two values left after all tokens are read do not constitute one complete result. Division by zero also needs an explicit error path; checking it before removing operands preserves the diagnostic state.
A stack evaluator can process tokens sequentially without repeatedly interpreting precedence brackets. Translators may emit a postfix or stack-oriented intermediate form after parsing source expressions.
RPN does not remove the need for valid syntax, supported operators or a correct parser. This exercise supports bounded numeric operands and binary +, −, × and /. Its infix conversion model deliberately excludes unary operators and function calls.
Worked example
| Token | Stack |
|---|---|
| 12 | [12] |
| 3 | [12,3] |
| − | [9] |
| 2 | [9,2] |
| / | [4.5] |
4 original questions total 12 marks. Attempt each before opening the independently written indicative marking guidance.
Convert (5+2)×(9−4) to RPN, and give the root operator and its two child subexpressions in the expression tree.
Indicative answer
Trace 20 5 / 3 − using real-number division. State the stack after each operator and reconstruct fully parenthesised infix.
Indicative answer
Explain separately why 4 +, 4 2, and 4 0 / fail as complete RPN calculations.
Indicative answer
AQA conversion practice: convert 8/2/2 to RPN under left association, and explain why 8 2 2 / / differs.
Indicative answer
This guide addresses AQA 7517 4.3.2.1; 4.3.3.1. Check your examination year and the complete specification for the assessment scope.
These are independently written explanations and practice questions. CompSciTutoring.co.uk is not affiliated with or endorsed by an examination board. The marking guidance is indicative; always check the syllabus for your examination year.
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