boolean-logic

Logic Gates

What is Boolean logic?

• Boolean logic is used in computer science and electronics to make logical decisions

• Boolean operators are either TRUE or FALSE, often represented as 1 or 0

• Inputs and outputs are given letters to represent them

• To define Boolean logic we use special symbols to make writing expressions much easier 

• In A Level Computer Science, Boolean algebra is easily confused with Boolean logic, but they are not the same

  • Boolean logic refers to the principles of logic based on binary values

  • Boolean algebra is a mathematical system used to manipulate Boolean values

Combination of Boolean operators

• Can be combined to form more complex expressions

• Use parentheses to clarify the order of operations
  Example: NOT (TRUE AND FALSE) = TRUE

Evaluating Boolean expressions

• There is a specific sequence for evaluating expressions with multiple operators just like in normal maths where BIDMAS applies

• Brackets come first then NOT then AND then OR

• Using Brackets can alter the standard order of operations

• Expressions within parentheses are evaluated first, following the same NOT, AND, OR precedence inside the parentheses

• Example: NOT (TRUE AND FALSE) equals NOT FALSE, which equals TRUE

Logic Gates

• Logic gates are a visual way of representing a Boolean expression

• The logic gates covered in this course are:

  • Conjunction (AND)

  • Disjunction (OR)

  • Negation (NOT)

  • Exclusive disjunction (XOR)

Conjunction (AND)

Operation	Circuit symbol	Notes
A ∧ B A . B		Returns TRUE only if both inputs are TRUE  TRUE AND TRUE = TRUE Otherwise = FALSE Next highest precedence after NOT Executes before OR operations

Disjunction (OR)

Operation	Circuit symbol	Explanation
A∨B A+B		Returns TRUE if either input is TRUE  TRUE OR FALSE = TRUE  FALSE OR FALSE = FALSE Lowest precedence in Boolean expressions Executes after NOT and AND operations

Negation (NOT)

Symbol	Circuit symbol	Notes
¬A		Inverts the input value NOT TRUE = FALSE NOT FALSE = TRUE Highest precedence in Boolean expressions Executes before AND and OR operations

Exclusive Disjunction (XOR)

Operation	Circuit symbol	Notes
AB A∨B		Outputs TRUE if the inputs are different Outputs FALSE if they are the same

Truth Tables

• A tool used in logic and computer science to visualise the results of Boolean expressions

• They represent all possible inputs and the associated outputs for a given Boolean expression

Conjunction (AND)