Boolean Logic Exam Practice (OCR J277 Paper 2 Style)

This lesson brings together everything from the Boolean Logic topic and provides exam-style practice for OCR J277 Paper 2 (Computational Thinking, Algorithms and Programming). Boolean logic questions appear in Paper 2 and can range from 1-mark recall questions to 6-mark extended response questions.

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What to Expect in the Exam

Boolean logic questions in OCR J277 Paper 2 may ask you to:

Question type	Typical marks	What you need to do
Identify a gate from a truth table	1-2	Name the gate that matches the given truth table
Complete a truth table	2-4	Fill in missing output values for a given circuit
Draw a logic circuit	2-3	Draw the gates for a given Boolean expression
Write a Boolean expression	2-3	Convert a circuit diagram or truth table to an expression
Trace through a circuit	3-4	Calculate the output for given inputs
Simplify an expression	2-3	Use Boolean algebra rules to simplify
Apply De Morgan's Laws	2-3	Rewrite an expression using De Morgan's Laws

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Practice Question 1: Gate Identification (1 mark)

A logic gate has the following truth table:

A	B	Q
0	0	1
0	1	0
1	0	0
1	1	0

State the name of this logic gate.

Answer: NOR gate

Explanation: The output is 1 only when both inputs are 0. This is the inverse of OR (which outputs 0 only when both inputs are 0).

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Practice Question 2: Truth Table Completion (3 marks)

Complete the truth table for the circuit: Q = (A AND B) OR (NOT C)

A	B	C	A AND B	NOT C	Q
0	0	0	0	1	1
0	0	1	0	0	0
0	1	0	0	1	1
0	1	1	0	0	0
1	0	0	0	1	1
1	0	1	0	0	0
1	1	0	1	1	1
1	1	1	1	0	1

OCR Exam Tip: Always include intermediate columns in your truth table working, even if the question does not explicitly ask for them. This shows your method and helps you avoid errors.

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Practice Question 3: Writing a Boolean Expression (2 marks)

Write the Boolean expression for a circuit where gate 1 is an AND gate with inputs A and B, and gate 2 is an OR gate with inputs from gate 1 and input C.

Answer: Q = (A AND B) OR C

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Practice Question 4: Circuit Tracing (3 marks)

A circuit implements the expression: Q = NOT(A OR B) AND C

Calculate the output Q when A = 0, B = 1, C = 1.

Step-by-step working:

1. A OR B = 0 OR 1 = 1
2. NOT(A OR B) = NOT 1 = 0
3. Q = 0 AND C = 0 AND 1 = 0

Answer: Q = 0

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Practice Question 5: De Morgan's Laws (2 marks)

Use De Morgan's Law to rewrite the expression NOT(A AND B).

Answer: (NOT A) OR (NOT B)

Explanation: De Morgan's first law states that NOT(A AND B) = (NOT A) OR (NOT B). The NOT is distributed to each variable, and AND changes to OR.

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Practice Question 6: Expression from Truth Table (3 marks)

Write a Boolean expression for the following truth table:

A	B	Q
0	0	1
0	1	0
1	0	0
1	1	1

Solution using sum of products:

• Row 1 (A=0, B=0): (NOT A) AND (NOT B)
• Row 4 (A=1, B=1): A AND B

Q = ((NOT A) AND (NOT B)) OR (A AND B)

This is the expression for XNOR (exclusive NOR) — the output is 1 when the inputs are the same.

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Practice Question 7: Simplification (3 marks)

Simplify the expression: (A AND B) OR (A AND NOT B)

Working:

• Factor out A: A AND (B OR NOT B)
• Apply complement law: B OR NOT B = 1
• Apply identity law: A AND 1 = A

Simplified expression: Q = A

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Decision Tree: Picking the Right Approach in the Exam

flowchart TD
    Q[Read the question] --> T{What is given?}
    T -->|Truth table only| SOP[Use sum of products: write a product term per row where Q=1, OR them together]
    T -->|Boolean expression| TT[Build a truth table by evaluating the expression for each input combination]
    T -->|Circuit diagram| TR[Trace gate by gate from inputs to output, then write the expression]
    T -->|Scenario in English| EX[Translate to AND/OR/NOT, then build a truth table]
    SOP --> S{Asked to simplify?}
    TT --> S
    TR --> S
    EX --> S
    S -->|Yes| LAW[Apply identity, complement, absorption, or De Morgan]
    S -->|No| FIN[Verify by substituting one row]
    LAW --> FIN
    FIN --> ANS[Write final answer with brackets]

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Exam Technique Checklist

When answering Boolean logic questions in OCR J277 Paper 2:

1. Read the question carefully — check whether it asks for a truth table, expression, circuit diagram, or simplification
2. Use systematic binary counting for truth tables (000, 001, 010, 011, 100, 101, 110, 111)
3. Show intermediate working — include intermediate columns in truth tables
4. Label your gates clearly in circuit diagrams
5. Use brackets to make the order of operations clear in expressions
6. Check your answer — substitute values back into your expression to verify it matches the truth table
7. Know your gate symbols — be able to recognise and draw all six gates

OCR Exam Tip: If you are unsure about a Boolean expression, construct a truth table to verify it. Even in simplification questions, you can check your simplified expression by confirming it produces the same outputs as the original.

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Key Facts to Memorise

Gate	Outputs 1 when...	Boolean symbol
NOT	Input is 0	Ā
AND	Both inputs are 1	A . B
OR	At least one input is 1	A + B
XOR	Inputs are different	A ⊕ B
NAND	Not both inputs 1	NOT(A . B)
NOR	Both inputs are 0	NOT(A + B)

De Morgan's Laws:

• NOT(A AND B) = (NOT A) OR (NOT B)
• NOT(A OR B) = (NOT A) AND (NOT B)

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Summary

• Boolean logic questions appear in OCR J277 Paper 2
• Questions range from 1-mark identification to multi-mark tracing and simplification
• Always show your working with intermediate columns
• Use the sum of products method to derive expressions from truth tables
• Verify answers by substituting values back into expressions
• Practise drawing all six gate symbols until you can do so from memory

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J277-Focused Reminder

OCR GCSE J277 examines only three operators: AND, OR, NOT. Although this lesson and earlier ones mention XOR, NAND, and NOR for completeness, your Paper 2 answers must use only AND, OR, NOT. Common scenarios rewritten into J277 form:

• "Exactly one of A, B is true" → (A . (NOT B)) + ((NOT A) . B) (not A XOR B)
• "Not both of A, B are true" → NOT (A . B) (not A NAND B)
• "Neither A nor B" → NOT (A + B) (not A NOR B)

If your truth table matches one of the "beyond spec" gates, always rewrite it in AND/OR/NOT form before committing your final answer.

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Extra Practice Question 8: Three-Input Circuit (4 marks)

A security system unlocks (U = 1) when a keycard is valid (K = 1) AND either a PIN is entered (P = 1) OR a fingerprint is recognised (F = 1).

(a) Write a Boolean expression for U.

(b) Complete the truth table.

Solution:

(a) U = K . (P + F).

(b)