Computer Programming Boolean Logic

What is Boolean Logic? Boolean logic is a system for determining the truth of a statement (or expression) based on whether certain variables are true or false. For example: In the statement, “I will go for a walk if it is sunny,” the decision is based on whether it is true that it is ‘sunny.’ 3 Trade & Industrial Education

Historical Note George Boole (1815-1864) was an English mathematician who devised a system of symbols and equations to represent logical decisions. Boolean Algebra was not widely used until the invention of computers. Boolean logic expressions are used to design electronic circuits and to represent decision-making in software. 4 Trade & Industrial Education

Use of Boolean Logic A combination of conditions, variables, and operators are used to determine if an expression is True or False. It can also be used to determine which elements can be members of a given set. Trade & Industrial Education

How are these categories different? Brown-eyed AND Male Brown-eyed OR Male Trade & Industrial Education

Who would be in these groups? NOT male AND wearing jeans NOT <16 Trade & Industrial Education

Like Mathematics, Boolean logic has operators Mathematic Operators + - x / = Trade & Industrial Education

Boolean Operators && ( AND ) || ( OR ) ! ( NOT ) Cheese || Pepperoni && !Anchovies Trade & Industrial Education

Boolean logic has an order of operations Mathematic Order of Operations is PEMDAS - Parentheses first Exponents next Multiplication and Division Addition and Subtraction. Trade & Industrial Education

Order of Boolean Operations Parentheses are not operators, but indicate grouping, consider these first. NOT (!) must be considered next. AND ( && ) is considered next. OR ( || ) is considered last. Trade & Industrial Education

!Tall && Blonde || Rich Consider the NOT first. !Tall is short. Consider the AND next. !Tall and Blonde, in other words, Short and Blonde. Consider the OR next. This person can be either Short and Blonde, or they can be Rich. They can also be Short, Blonde, and Rich. Trade & Industrial Education

Order of Operations Parentheses first, then NOT (!) , then && , then || !Tall && Blonde || Rich !(Tall && Blonde) || Rich !Tall && !Blonde || Rich Trade & Industrial Education

Venn Diagrams Venn Diagrams can be used to visualize Boolean expressions. Trade & Industrial Education

Venn Diagram A B A && B Trade & Industrial Education

Where is !A A B Trade & Industrial Education

Where is A || B ? A B Trade & Industrial Education

Truth Tables Truth tables are used to evaluate possible combinations of variables and operators. Trade & Industrial Education

A || B (A OR B) A B A || B True False Trade & Industrial Education

A && B (A AND B) A B A && B True False Trade & Industrial Education

!A (NOT A) A !A True False Trade & Industrial Education

!A || B (NOT A OR B) A B !A || B True False Trade & Industrial Education

Check for Understanding Determining the results of a Boolean expression is known as evaluating it. All Boolean expressions evaluate to either True or False. Trade & Industrial Education

Evaluate: What would be printed, A or B? boolean blonde = false; if ( blonde) System.out.println(“A”); if ( !blonde) System.out.println(“B”); Trade & Industrial Education

Evaluate: What would be printed, A or B? boolean tall = false; boolean male = true; if ( male && tall) System.out.println(“A”); if ( male || tall) System.out.println(“B”); Trade & Industrial Education

Evaluate: What would be printed, A or B? boolean x = false; boolean y = true; if ( x && y) System.out.println(“A”); if ( !x && y) System.out.println(“B”); Trade & Industrial Education

Shade in A || !B A B Trade & Industrial Education

Shade in A && !B A B Trade & Industrial Education

Shade in !A && !B A B Trade & Industrial Education

Will it print? boolean x = true; boolean y = false; if ( x && !y) System.out.print(“A”); Trade & Industrial Education

Will it print? boolean x = true; boolean y = false; if (! x || y) System.out.print(“A”); Trade & Industrial Education

With what you know… Can you evaluate a boolean expression? Trade & Industrial Education