Boolean Logic

Exam Practice Questions

These questions are styled exactly like the ones in the real exam. Write your full answer before revealing the mark scheme. Truth table questions in particular reward method — show intermediate columns.

Short answer questions

Write your answer in full before revealing the mark scheme. These test recall of gate rules and truth table structure.

Question 12 marksGate recall

State the rule for an AND gate and give the output when A = 1 and B = 0.

Write your answer here...

Mark scheme

An AND gate outputs 1 only when all inputs are 1 [1 mark]

When A = 1 and B = 0, the output is 0 [1 mark]

Note: Accept "the output is 1 only if both inputs are 1" or equivalent. Do not accept "if one input is 1" — this describes OR.

Question 24 marksTruth table

Complete the truth table for an XOR gate with inputs A and B. State one way in which XOR differs from OR.

Complete the table below, then state the difference:

A | B | Q (A XOR B)
0 | 0 | ___
0 | 1 | ___
1 | 0 | ___
1 | 1 | ___

Mark scheme

A	B	Q (XOR)
0	0	0
0	1	1
1	0	1
1	1	0

All four output values correct [2 marks — lose 1 per error, min 0]

XOR outputs 0 when both inputs are 1 / OR outputs 1 when both inputs are 1 [1 mark]

XOR outputs 1 only when exactly one input is 1 (exclusive) [1 mark]

Note: For the difference, accept any correct statement distinguishing XOR from OR in the case where both inputs are 1.

Question 32 marksUniversal gate

Explain what is meant by a "universal gate" and state one example.

Write your answer here...

Mark scheme

A universal gate is one from which any other logic gate can be constructed using only that gate type [1 mark]

NAND (or NOR) is a universal gate [1 mark]

Note: Both NAND and NOR are correct. Do not accept XOR, AND, OR or NOT — these are not universal.

Logic circuit questions

These require a full method. Show all intermediate columns in your truth table. Write your answer before revealing the mark scheme.

Question 45 marksCircuit analysis

A logic circuit has inputs A and B. Input A passes through a NOT gate to produce NOT A. NOT A and B are then fed into an OR gate to produce the output Q.

(a) Write the Boolean expression for Q. [1 mark]
(b) Complete the full truth table for Q, including an intermediate column for NOT A. [4 marks]

Write your Boolean expression and complete the truth table before revealing...

Mark scheme

(a) Q = (NOT A) OR B [1 mark]

A	B	NOT A	Q = (NOT A) OR B
0	0	1	1
0	1	1	1
1	0	0	0
1	1	0	1

Intermediate NOT A column correct [1 mark]

All four Q values correct [2 marks — lose 1 per error]

All four input combination rows present in the correct order [1 mark]

Note: The output Q = (NOT A) OR B is 0 only when A = 1 and B = 0. In all other cases the output is 1. Many students get the third row wrong — they apply OR to the original A (which is 1) rather than to NOT A (which is 0).

Question 56 marksThree-input circuit

A logic circuit has three inputs: A, B and C. The circuit is described as: inputs A and B enter an AND gate to produce signal P. Input C passes through a NOT gate to produce NOT C. P and NOT C then enter an OR gate to produce the output Q.

(a) Write the Boolean expression for Q. [2 marks]
(b) Complete the truth table including intermediate columns for P and NOT C. [4 marks]

This has 3 inputs — how many rows? Write the expression and complete the table before revealing...

Mark scheme

(a) P = A AND B [1 mark]; Q = P OR (NOT C) = (A AND B) OR (NOT C) [1 mark]

A	B	C	P = 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

All eight rows present in correct binary order [1 mark]

Intermediate columns P and NOT C correct throughout [1 mark]

Q column correct: Q = 0 only when P = 0 AND NOT C = 0, i.e. when A AND B = 0 AND C = 1 [2 marks — 1 per two correct rows]

Note: Q is 0 only in rows where C = 1 and A AND B = 0 (rows 2, 4, 6). Q is 1 when either A AND B = 1 (rows 7, 8) or C = 0 (rows 1, 3, 5).

Question 63 marksDescribe / evaluate

Evaluate the expression Q = NOT (A AND B) for all four input combinations. Identify which type of gate produces this output.

Evaluate all four rows and identify the gate type...

Mark scheme

A	B	A AND B	Q = NOT(A AND B)
0	0	0	1
0	1	0	1
1	0	0	1
1	1	1	0

All four Q values correct: 1, 1, 1, 0 [2 marks — 1 if three correct]

This is a NAND gate [1 mark]

Note: NOT (A AND B) is the definition of NAND. Students may also state that NAND is an AND gate with its output inverted — accept this phrasing.

Back to Boolean Logic series Review Lesson 1 Review Lesson 3