Paper Gem - Unit 2.4 Boolean Logic (Maths & Circuits)

Question 1 [4 Marks]

The following truth table represents the expression: Q = ¬A ∨ B
Complete the truth table.

[4]

A	B	¬A (NOT A)	Q
0	0
0	1
1	0
1	1

A	B	¬A (NOT A)	Q
0	0
0	1
1	0
1	1

✅ Mark Scheme

Column ¬A: 1, 1, 0, 0 (1)
Column Q: 1, 1, 0, 1 (2 for all correct, 1 for 2/4 correct)

Score:

Question 2 [3 Marks]

Match the mathematical expression to the correct English description.
Draw a line (or write the letter pair) to connect them.

[3]

Expression		Description
A. A ∧ B		1. A OR B
B. ¬A		2. A AND B
C. A ∨ B		3. NOT A

Draw your answer below:

✅ Mark Scheme

A -> 2 (AND)
B -> 3 (NOT)
C -> 1 (OR)

Score:

Question 3 [5 Marks]

Complete the truth table for the logic expression:
P = (A AND B) OR C
Tip: Calculate the bracket (A AND B) first.

[5]

A	B	C
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

A	B	C
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

✅ Mark Scheme

Intermediate (A AND B): Last 4 rows: 0, 0, 1, 1 (1)
Final P (Rows 1-4): 0, 1, 0, 1 (1)
Final P (Rows 5-8): 0, 1, 1, 1 (1)
(Award 2 additional marks if table is perfectly correct).

Score:

Question 4 [1 Marks]

A student has attempted to complete a truth table for the expression P = NOT (A OR B).
Their answer is shown below. They have made two mistakes.

Student's Incorrect Work:

A	B	A OR B	P
0	0	0	1
0	1	1	0
1	0	0	1
1	1	1	0

(i) Identify the Row number where the first error occurs in the calculation.

[1]

(ii) Explain why the value in the final column (P) for Row 3 is considered incorrect based on the student's working, even if the math seems right for that step.

[1]

(iii) State the correct Final Output for Row 3.

[1]

(i)

(ii)

(iii)

✅ Mark Scheme

(i) Row 3 (Input A=1, B=0, A OR B should be 1). (1)
(ii) The student calculated NOT(0) to get 1. They lose the mark because the logic gate A OR B was processed incorrectly first. (1)
(iii) Correct Output: 0 (1)

Score:

Question 5 [1 Marks]

A security light system has two inputs:
M: Motion Detected (1 = Motion, 0 = No Motion)
N: Night Time (1 = Night, 0 = Day)
The system is designed so the light turns ON (1) only when Motion is detected AND it is Night time.

(i) Look at the Truth Table below. Does this table correctly represent the system described above?
Write YES or NO.

M	N	Light
0	0	0
0	1	1
1	0	1
1	1	1

[1]

(ii) Justify your answer.

[2]

Part 1

Part 2

Part 3

✅ Mark Scheme

(i) NO (1)
(ii) The table shows an OR gate (Light on if M OR N is true). The scenario requires an AND gate (Light on ONLY if M AND N are true). (2)

Score:

Question 6 [4 Marks]

Consider a logic circuit configured as follows:

Input A and Input B go into an OR gate.
The output of that OR gate goes into an AND gate.
Input C goes into the other connection of that AND gate.

Complete the final two rows of the truth table for this circuit.

[4]

A	B	C	A OR B	Final Output
...	...	...	...	...
1	1	0
1	1	1

A	B	C	A OR B	Final Output
...	...	...	...	...
1	1	0
1	1	1

✅ Mark Scheme

Row (1, 1, 0): A OR B = 1. Final Output = 0 (1 AND 0). (2)
Row (1, 1, 1): A OR B = 1. Final Output = 1 (1 AND 1). (2)

Score: