Welcome to Lesson 9!

Announcements

• Midterm after a short lesson and the break
  
• Don't forget Assignment 8 due Monday!
  
• Don't forget Lab 5 due Friday!
  

Logical Operators

• In certain situations, we may wish to use more than one test condition inside of an if statement.
• To do so, we will need to chain the test conditions together using logical operators (either && or ||)
  
• For example, recall our guessing game program:

Review of Boolean Variables

• Sometime we need to evaluate a logical condition in one part of a program and use it elsewhere
• To store a condition that can only be true or false, we use a Boolean variable
• Boolean variables are named after George Boole (1815-1864), a pioneer in the study of logic
• We specify a Boolean variable using the bool type, which can hold just one of two values: true or false

  bool isCool = true;
  bool lies = false; 
  

Test Conditions and Boolean Values

• Remember that test conditions always evaluate to true or false

  if (num > 0)
  

• Thus we can use a boolean variable as a test condition

  bool isPositive = (num >= 0);
  if (isPositive)
  

• Note that we do not need to add a relational expression to a boolean variable, like:

  if (isPositive == true) // avoid!

• Since the boolean variable already evaluates to true or false, adding the == true is redundant
• Likewise, we do not need to use:

  if (isPositive != false) // avoid!

• If we want to reverse the test condition, we can use the not (!) operator

  if (!isPositive)

• We can see the use of a boolean variable in the following example

Example Application Using a Boolean Variable

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

#include <iostream>
using namespace std;
int main() {
    double num;
    cout << "Enter a number: ";
    cin >> num;

    bool isPositive = (num >= 0);
    cout << boolalpha << "The test evaluated to: " << isPositive << endl;
    if (isPositive) {
        cout << "The number was 0 or positive\n";
    } else {
        cout << "The number was negative\n";
    }
}

Introducing &&, || and !

Logical operators and search engines video

Combining Test Conditions with Logical Operators

• A logical operator, or boolean operator, is an operator that treats operands as boolean values (true or false)
• C++ has several logical operators, but we only need to use three to create any possible test condition
• These three operators are and, or and not, which are discussed below
• These logical operators are traditionally written as && (and), || (or) and ! (not)

Truth Tables for AND, OR and NOT

&& (AND) Operator Truth Table

expr1	expr2	expr1 && expr2	Example	Result
true	true	true	5 < 10 && 5 > 2	true
true	false	false	5 < 10 && 5 < 2	false
false	true	false	5 > 10 && 5 > 2	false
false	false	false	5 > 10 && 5 < 2	false

|| (OR) Operator Truth Table

expr1	expr2	expr1 || expr2	Example	Result
true	true	true	5 < 10 or 5 > 2	true
true	false	true	5 < 10 or 5 < 2	true
false	true	true	5 > 10 or 5 > 2	true
false	false	false	5 > 10 or 5 < 2	false

not (!) Operator Truth Table

If expr is...	Then ! expr is...	Example	Result
true	false	!true	false
false	true	!(5 < 2)	true

Testing Multiple Conditions Using Logical Operators

• Sometimes we need to test for multiple conditions using a single if statement
  
• In this case, we will need to chain together the two conditions using a logical operator, either && or ||
• Note that one either side of the logical operator there must be a stand alone test condition

if (age >= 18 && age <= 25) //Correct!!!

if (age >= 18 && <= 25) //No! Incorrect!!

• For example, we want to test if an age is between 18 and 65
• We need to test that both parts of are true: that the age is >= 18 AND that the age is <= 65
  

int age = 0;
cout << "Enter your age: ";
cin >> age;
if (age >= 18 && age <= 65)
{
    cout << "Adult!\n";
} else {
    cout << "Child, Teen or Older Adult!\n";
}

• Another way to use logical operators to test the age is:

  int age = 0;
  cout << "Enter your age: ";
  cin >> age;
  if (age < 18 || age > 65)
  {
      cout << "Child, Teen or Older Adult!\n";
  } else {
      cout << "Adult!\n";
  }
  

• Many people confuse && and || conditions, especially when learning about logical operators
• A value lies between 18 and 65 if the value is at least 18 and at most 65
  
• A value is outside that range if it is less than 18 or greater than 65
  
• There is no golden rule; we have to think carefully and test our conditions

Parenthesis

• Remember that a Boolean expression in an if statement must be enclosed in parenthesis
• Thus, an if statement with && might look like:

  if ((guess != GUESS1) && (guess != GUESS2))

• However, relational operators have a higher precedence than logical operators
• Thus, we can remove the inner parenthesis without affecting the meaning:

  if (guess != GUESS1 && guess != GUESS2)

• However, if using parenthesis is easier to understand then use the extra parenthesis

More Information on Logical Operators

• Domino Addition - Numberphile: Logical operator circuits using dominoes