Boolean Logic: Gates and Truth Tables

A logic gate is a circuit component that takes one or more binary inputs (0 or 1) and produces a single binary output according to a fixed rule. Digital computers are built from billions of these gates.

The output of each gate is determined entirely by its inputs — there is no analogue gradation. Logic gates are the physical implementation of Boolean algebra, a mathematical system where values are either true (1) or false (0).

AQA 8525 requires knowledge of four gates:

Gate	Inputs	Core rule
NOT	1	Inverts the input
AND	2 or more	Output is 1 only if all inputs are 1
OR	2 or more	Output is 1 if at least one input is 1
XOR	2	Output is 1 if inputs are different

NAND and NOR gates are explicitly excluded from AQA 8525. Do not use them in answers unless the question supplies them.

Logic gates underpin all digital processing — from the arithmetic logic unit (ALU) inside a CPU to the condition checks in every if statement.

The NOT gate (also called an inverter) takes one input and produces its opposite. If the input is 1, the output is 0; if the input is 0, the output is 1.

Boolean notation: $\bar{A}$ (A with an overbar, read "NOT A")

Truth table:

A	$\bar{A}$ (NOT A)
0	1
1	0

The NOT gate is the only single-input gate in AQA 8525. The circuit symbol is a triangle pointing right with a small circle (bubble) at the output.

Worked example — evaluate $\bar{A}$ for both input values:

• A = 0 → NOT gate inverts → output = 1
• A = 1 → NOT gate inverts → output = 0

A truth table for a single-input gate always has exactly 2 rows ($2^1=2$ input combinations). For 2 inputs: 4 rows. For 3 inputs: 8 rows.

The overbar in Boolean algebra ($\bar{A}$) means "the complement of A". It always produces the opposite of A's current value.

AND gate — output is 1 only when all inputs are 1. If any input is 0, the output is 0.

OR gate — output is 1 when at least one input is 1. Output is 0 only when all inputs are 0.

Boolean notation:

• AND: $A\cdot B$ (written A.B)
• OR: $A+B$ (written A+B)

Truth tables (two inputs):

A	B	A.B (AND)	A+B (OR)
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	1

AND produces a 1 in only one row (both inputs 1). OR produces a 1 in three rows (anything except both 0).

Worked example — evaluate $A\cdot B+\bar{C}$ where A = 1, B = 0, C = 1:

1. $A\cdot B$ = 1 AND 0 = 0
2. $\bar{C}$ = NOT(1) = 0
3. $0+0$ = 0 OR 0 = 0 → final output = 0

AND is the stricter gate — all inputs must be 1. OR is more permissive — just one 1 is enough.