Computers are all about binary - 1's and 0's, on and off, true and false. A large part of writing logic with our programs is all about asking "yes/no" questions. If "criteria" is true, then execute this code… if it's false, execute that code. In order to better understand how branching works in our programs, it's important to learn about boolean logic.

"Boolean" refers to something that is either true or false. This can be the values "true" and "false" itself, or it can be an expression that evaluates to true or false. For example:

• if (the user clicked "save") then…
• if (the account balance is less than 0) then…
• if (the "done" variable is set to true) then…

The statements within the parentheses are the boolean expressions, and then we can use those expressions in if statements and while loops to execute code only if that condition evaluates to true.

x and y can be swapped out with different types of data. We can check if two strings of text are equal, or if two numbers are equal. With the bottom two examples, "is x?" and "is not x?" applies for if x is a boolean variable - a variable that is storing a value of either true or false.

if ( i_have_not_been_fed && it_is_6_am ) {
  MakeLotsOfNoise();
}

We can also create compound boolean expressions from separate boolean expressions using logic operators. Logic operators are AND (&&), OR (||), and NOT (!).

• Is x == y and x == z?
  • In C++ code: x = y && x = z
  • True if both sub-expressions are true (x==y and x==z).
  • False if one or both sub-expressions are false.

if ( wantsBeer && isAtLeast21 && likesBeer ) {
    GiveBeer();
}

• Is x == y or x == z?
  • In C++ code: x = y || x = z
  • True if at least one sub-expression is true.
  • False if both sub-expressions are false.

if ( isBaby || isSenior || isVet )
{
    GiveDiscount();
}

• Is x false?
  • In C++ code: !x
  • True if the sub-expression is false.
  • False is the sub-expression is true.

// Just checking documentSaved is true
if ( documentSaved ) {
    Quit();
}

// Checking if documentSaved is false
if ( !documentSaved ) {
    Save();
    Quit();
}

We can have boolean variables that store true or false, and we can then do tests on those values…

bool quit = false;

// ( pretend there's more code here )

if ( quit ) // If quit is true
{
    return 0; // exit
}

But we can also create boolean expressions by utilizing those relational operators to compare two values together.

float balance;
cout << "Enter your bank balance: ";
cin >> balance;

if ( balance < 0 ) // balance < 0 will return true or false
{
    cout << "OVERDRAWN!" << endl;
}

These relational operators can also work on strings, where < and > will check alphabetical order (sort of).

string student1, student2;

cout << "Enter student 1 name: ";
getline( cin, student1 );

cout << "Enter student 2 name: ";
getline( cin, student2 );

if ( student1 < student2 )
{
    cout << "Student 1 goes first" << endl;
}
else
{
    cout << "Student 2 goes first" << endl;
}

Note that when using < and > with strings or chars, it will compare them based on alphabetical order - if they're both the same case (both uppercase or both lowercase). The code 65 represents 'A', but the code 97 represents 'a', so items will be "sorted" based on these codes.

We can use truth tables to help us visualize the logic that we're working with, and to validate if our assumptions are true. Truth tables are for when we have an expression with more than one variable (usually) and want to see the result of using ANDs, ORs, and NOTs to combine them.

In order to be able to write if statements or while loops, you need to understand how these boolean expressions work. If you're not familiar with these concepts, they can lead to you writing logic errors in your programs, leading to behavior that you didn't want.