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.
(i) Q = ¬ A
(ii) Q = A ∧ B
(iii) Q = A ∨ B

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

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.

A	B	P
0	0
0	1
1	0
1	1

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).

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

A	B	C	(A OR B)	Q
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 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.

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:
(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).