Paper Gem - Unit 2.4 Boolean Logic

Question 1 [3 Marks]

The J277 specification allows for the use of standard mathematical notation for logic gates.
Calculate the output (Q) for the following expressions when Input A = 1 and Input B = 0.

[3]

(i) Q = ¬ A

(ii) Q = A ∧ B

(iii) Q = A ∨ B

(i)

(ii)

(iii)

✅ Mark Scheme

(i) 0 (1)
(ii) 0 (1)
(iii) 1 (1)

Score:

Question 2 [2 Marks]

A student has written the logic expression: P = NOT (A AND B)
Rewrite this expression using only the mathematical symbols (∧, ∨, ¬).

[2]

Part 1

Part 2

✅ Mark Scheme

P = ¬(A ∧ B)

Score:

Question 3 [4 Marks]

Consider the following logic circuit described in text form:

Input A goes into a NOT gate.
The output of that NOT gate goes into the top input of an AND gate.
Input B goes directly into the bottom input of that same AND gate.
The output of the AND gate is P.

Complete the truth table for this circuit.

[4]

A	B	P
0	0
0	1
1	0
1	1

A	B	P
0	0
0	1
1	0
1	1

✅ Mark Scheme

1 mark for every correct row:
0 0 -> 0
0 1 -> 1
1 0 -> 0
1 1 -> 0

Score:

Question 4 [4 Marks]

A smart heating system turns on the heater (H) only if the following conditions are met:

The Main Power Switch (S) is ON.
AND
Either the Temperature (T) is Cold OR the Override Button (O) is pressed.

Draw the logic circuit for this system.
Use standard OCR symbols (Triangle with circle for NOT, D-shape for AND, Shield/Arrow for OR).

[4]

Draw your answer below:

✅ Mark Scheme

Score:

Question 5 [5 Marks]

Complete the truth table for the expression: Q = (A OR B) AND C

[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

(A OR B) Column: 0, 0, 1, 1, 1, 1, 1, 1 (1)
Q Column Rows 1-4: 0, 0, 0, 1 (1)
Q Column Rows 5-8: 0, 1, 0, 1 (1)
(2 marks for fully correct table with no errors)

Score:

Question 6 [2 Marks]

A student attempts to draw a logic circuit involving a NOT gate. They draw a single triangle without a small circle at the point.

Explain why the examiner will award 0 marks for this specific gate, even if the logic flow is correct.

[2]

Part 1

Part 2

✅ Mark Scheme

A triangle without a circle represents a Buffer (1), which passes the signal unchanged / does not invert the signal (1).

Score:

Question 7 [4 Marks]

Look at the logic expression: P = A AND B OR C.
The student claims the order of operations does not matter.

Using inputs A=0, B=1, C=1:

[4]

(a) Calculate the output if you do AND first.

(b) Calculate the output if you do OR first.

(c) State which operator has precedence in Boolean logic (which one happens first).

(a)

(b)

(c)

✅ Mark Scheme

(a) AND First: (0 AND 1) = 0 -> (0 OR 1) = 1 (1)
(b) OR First: (1 OR 1) = 1 -> (0 AND 1) = 0 (1)
(c) Precedence: NOT, then AND, then OR. (1)

Score: