A Boolean value has one of two states: True or False, which can also be represented as 1 and 0 respectively.
Boolean logic combines and processes True and False values according to logical rules.
Logic gates operate on Boolean inputs and produce a single Boolean output.
The three main logic gates are \text{AND}, \text{OR}, and \text{NOT}.
\text{AND} and \text{OR} gates have two inputs, while a \text{NOT} gate has one input.

Logic diagrams use symbols to show how Boolean values pass through logic gates.
Inputs are usually labelled with letters such as A, B, and C, while outputs may be labelled P or Q.
The output of a logic gate depends on the current value or values supplied to its input or inputs.
An \text{AND} gate produces an output of 1 only when both inputs are 1.
If either input to an \text{AND} gate is 0, the output is 0.
An \text{OR} gate produces an output of 1 when at least one input is 1.
An \text{OR} gate produces an output of 0 only when both inputs are 0.
A \text{NOT} gate has one input and reverses its value.
A \text{NOT} gate changes 0 to 1 and 1 to 0.

A truth table shows every possible combination of input values for a logic system and the output produced for each combination.
A complete truth table must include every possible input combination exactly once.
In an \text{AND} truth table, the output is 1 only when both inputs are 1.
In an \text{OR} truth table, the output is 1 when at least one input is 1 and is 0 only when both inputs are 0.
A \text{NOT} truth table has one input and two possible rows: 0 produces 1, and 1 produces 0.
A truth table with n inputs contains 2^n rows of input combinations.

Logic gates can be connected so that the output of one gate becomes an input to another.
Combined Boolean expressions should be evaluated one stage at a time.
The normal order of precedence is \text{NOT}, then \text{AND}, then \text{OR}, unless brackets specify a different order.
Brackets are evaluated before the rest of a Boolean expression.
A Boolean expression can be obtained from a logic diagram by following the gates from the inputs towards the final output.
A logic diagram can be constructed from a Boolean expression by breaking the expression into individual operations, starting with the innermost brackets where present.

To apply Boolean logic to a problem, identify the conditions that can each be True or False and assign each condition a Boolean input.
The conditions are then combined using Boolean operators to produce the required output.
A written set of rules can be translated into Boolean inputs, represented as a Boolean expression, and evaluated using a truth table.

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