2.4 Boolean logic

Boolean logic

A form of algebra where all values are either TRUE (1) or FALSE (0), used in computers to control decision-making and logical operations.

Truth table

A table used to show the output of Boolean expressions for all possible input combinations, useful for debugging and understanding logic conditions.

Logic gates

Components in a computer's processor that apply logical operations to one or more Boolean inputs to produce a single output.

AND gate

Returns TRUE only if both inputs are TRUE; symbol: A AND B, A ∧ B.

OR gate

Returns TRUE if either input is TRUE; symbol: A OR B, A ∨ B.

NOT gate

Reverses the input; symbol: NOT A, ¬A.

Combining operators

The process of combining logic gates to build expressions like A AND (B OR NOT C), A ∧ (B ∨ ¬C).

Order of precedence

The rule that some operations must be applied before others, similar to BODMAS in Mathematics.

Logic circuit symbols

Internationally recognized symbols for logic gates that have inputs on the left and outputs on the right.

Logic circuit diagrams

Diagrams that combine logic gates to form more complex circuits, which can be drawn or interpreted.

Example 1 - combining two AND gates

The output Q is TRUE only if A, B AND C are all TRUE; Boolean expression: A AND B AND C.

Example 2 - combining NOT and OR gates

The output Q is TRUE when either A is FALSE, B is TRUE, or both.

Operator precedence

The ranking of operations in Boolean algebra, where Brackets have the highest precedence, followed by NOT, AND, and OR.

A AND B

The result of the AND operation between inputs A and B.

A OR B

The result of the OR operation between inputs A and B.

NOT A

The result of the NOT operation applied to input A.

Binary addition

A more complex operation that can be performed by combined logic circuits.

Inputs

The values fed into logic gates, which can be either TRUE (1) or FALSE (0).

Outputs

The result produced by logic gates based on the inputs.

Logical operations

Operations that manipulate Boolean values, such as AND, OR, and NOT.

Debugging

The process of identifying and fixing errors in logic conditions using truth tables.

Complex operations

Operations that require the combination of multiple logic gates.