3.4.2 Boolean Logic — AQA 8525

What Is Boolean Logic?

Boolean logic is a system of logic where values can only be TRUE (1) or FALSE (0). It is the foundation of how computers process data — every bit in a computer is either 0 or 1, and Boolean operations are performed by logic gates built into the CPU's ALU.

AQA requires knowledge of three gates: AND, OR, and NOT.

Logic Gates and Truth Tables

AND Gate

Output is 1 only if ALL inputs are 1. Like a series circuit — every switch must be closed.

A AND B

A	B	Output
0	0	0
0	1	0
1	0	0
1	1	1

Memory: AND = all must be true

OR Gate

Output is 1 if AT LEAST ONE input is 1. Like a parallel circuit — any switch closes the circuit.

A OR B

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1

Memory: OR = any will do

NOT Gate

Inverts the input. One input only. Also called an inverter.

NOT A

A	Output
0	1
1	0

Memory: NOT = flip it

Boolean Expressions

Logic circuits can be described using Boolean expressions:

Gate	Boolean expression	AQA notation
AND	A AND B	A · B or A AND B
OR	A OR B	A + B or A OR B
NOT	NOT A	Ā or NOT A

Combining Gates — Logic Circuits

Multiple gates can be combined into a logic circuit. To find the output, evaluate each gate in turn from left to right (inputs to output).

Example: X = (A AND B) OR (NOT C)

Inputs: A=1, B=0, C=1 Step 1: A AND B = 1 AND 0 = 0 Step 2: NOT C = NOT 1 = 0 Step 3: 0 OR 0 = 0 Output X = 0

Truth Tables for Combined Expressions

For n inputs, a truth table has 2ⁿ rows. List inputs in binary counting order (000, 001, 010, ...). Add intermediate columns to work out complex expressions.

Example truth table: Q = NOT A AND B

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

Exam tip: The most common marks are for completing truth tables. Always use 2ⁿ rows, always list inputs in binary order (00, 01, 10, 11 for 2 inputs). Add intermediate columns (e.g. NOT A) to avoid errors in complex expressions. Never skip rows.

⚠️ Common Mistakes

AND — only 1 when ALL inputs are 1, not just some
OR — output is 1 even when BOTH inputs are 1 (students often write 0 for 1,1 OR)
Missing rows in truth tables — 3 inputs need 8 rows (2³), not 6
Applying NOT after the AND/OR without brackets — always evaluate what's inside brackets first

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Key points

Boolean logic: values are only 0 (false) or 1 (true)
AND gate: output 1 only if ALL inputs are 1
OR gate: output 1 if ANY input is 1
NOT gate: inverts the input (0→1, 1→0)
Truth tables: 2ⁿ rows for n inputs; always binary counting order
Combined circuits: evaluate gate by gate from inputs to output

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Worksheet — 3.4.2 Boolean Logic

8 questions · 20 marks

Q1State the output of an AND gate when A=1, B=0.[1]

✅ Mark scheme

Mark scheme

0 — AND requires both inputs to be 1 [1].

Q2State the output of an OR gate when A=1, B=1.[1]

✅ Mark scheme

Mark scheme

1 — OR outputs 1 if at least one input is 1 (including when both are 1) [1].

Q3Complete the truth table for: Q = A OR (NOT B)[4]

✅ Mark scheme

Mark scheme

Row (0,0): NOT B=1, Q=1 [1]; Row (0,1): NOT B=0, Q=0 [1]; Row (1,0): NOT B=1, Q=1 [1]; Row (1,1): NOT B=0, Q=1 [1].

Q4Complete the full truth table for: Q = (A AND B) OR C. How many rows?[5]

✅ Mark scheme

Mark scheme

8 rows (2³) [1]; A AND B column: 0,0,0,0,0,0,1,1 [1]; Q column: 0,1,0,1,0,1,1,1 [2]. (Award 2 for fully correct Q column, 1 for 6/8 correct)

Q5Evaluate (A AND B) OR (NOT C) when A=1, B=1, C=0. Show all steps.[3]

✅ Mark scheme

Mark scheme

A AND B = 1 AND 1 = 1 [1]; NOT C = NOT 0 = 1 [1]; 1 OR 1 = 1, so output = 1 [1].

Q6What is the only row in a two-input AND truth table where the output is 1?[1]

✅ Mark scheme

Mark scheme

A=1, B=1 [1].

Q7Explain, using Boolean logic, how a smart door lock could work: the door opens if the correct PIN is entered AND (the door is unlocked OR the manager override is active).[3]

✅ Mark scheme

Mark scheme

Let P=correct PIN, U=door unlocked, M=manager override. Expression: Open = P AND (U OR M) [1]; if P=0 (wrong PIN), door never opens regardless of U or M [1]; if P=1 and either U=1 or M=1, door opens [1].

Q8Describe how logic gates relate to transistors inside a CPU.[2]

✅ Mark scheme

Mark scheme

Logic gates are implemented physically using transistors [1]; transistors act as electronic switches (on=1, off=0) that can be combined to form AND, OR, and NOT gates inside the CPU's ALU and other circuits [1].

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What Is Boolean Logic?

Logic Gates and Truth Tables

AND Gate

OR Gate

NOT Gate

Boolean Expressions

Combining Gates — Logic Circuits

Truth Tables for Combined Expressions

Key points

Worksheet — 3.4.2 Boolean Logic

Mini Test — 3.4.2 Boolean Logic