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3.1. Boolean Expressions

Boolean variables or expressions can only have true or false values.

3.1.1. Testing Equality (==)

Primitive values like ints and reference values like Strings can be compared using the operators == and != (not equal) to return boolean values. The expression x == 4 evaluates to true if the memory location for variable x currently stores the value 4, otherwise the expression is false. Note that x == 4 does not assign a value to variable x, rather it simply compares the value of x to 4.

Note

The operator = changes the value of a variable. The operator == tests if a variable holds a certain value, without changing its value!

Coding Exercise

What will the code below print out? Try to guess before you run it! Note that 1 equal sign (=) is used for assigning a value and 2 equal signs (==) for testing equality between values. The != operator tests for inequality.

public class BoolTest1 { public static void main(String[] args) { int age = 15; int year = 14; // Will this print true or false? System.out.println( age == year ); year = 15; // Will this print true or false? System.out.println( age == year ); // Will this print true or false? System.out.println( age != year ); } }

We can also use == or != to test if two reference values, like Turtle and String objects, refer to the same object. In the figure below, we are creating two separate Turtle objects called juan and mia. They do not refer to same object or turtle. Then, we create a reference variable called friend that is set to mia. The turtle mia will have two ways (references or aliases) to name her – she’s both mia and friend, and these variables refer to the same object (same Turtle) in memory. If two reference variables refer to the same object like the turtle on the right in the image below, the test with == will return true which you can see in the code below.

Figure 1: Turtle Reference Equality

Coding Exercise

What will the code below print out? Try to guess before you run it!

import java.util.*; import java.awt.*; public class BoolTestRef { public static void main(String[] args) { World world = new World(300,300); Turtle juan = new Turtle(world); Turtle mia = new Turtle(world); // Will these print true or false? System.out.println(juan == mia); Turtle friend = mia; // set friend to be an alias for mia System.out.println(friend == mia); } }

3.1.2. Relational Operators (<, >)

The Relational Operators below in Java are used to compare numeric values or arithmetic expressions. Although some programming languages allow using relational operators like < to compare strings, Java only uses these operators for numbers, and uses the string methods compareTo() and equals() for comparing String values.

• < Less Than

• > Greater Than

• <= Less than or equal to

• >= Greater than or equal to

• == Equals

• != Does not equal

With <= and >=, remember to write the two symbols in the order that you would say them “less than” followed by “or equal to”.

Coding Exercise

Try to guess what the code below will print out before you run it.

public class BoolTest2 { public static void main(String[] args) { int age = 15; int year = 14; // Will these print true or false? System.out.println( age < year ); System.out.println( age > year ); System.out.println( age <= year+1 ); System.out.println( age-1 >= year ); } }

Check your understanding

3-1-4: Drag the boolean expression from the left and drop it on what it is testing on the right. Click the "Check Me" button to see if you are correct. Review the relational operators above.
• x > 0
• x is positive
• x == y
• x equals y
• x < 0
• x is negative
• x != y
• x does not equal y
• x < y
• x is less than y
• x > y
• x is greater than y
• x >= y
• x is greater than or equal to y

3.1.3. Testing with mod (%)

Here are some boolean expressions that are very useful in coding:

// Test if a number is positive
(number > 0)
//Test if a number is negative
(number < 0)
//Test if a number is even by seeing if the remainder is 0 when divided by 2
(number % 2 == 0)
//Test if a number is odd by seeing if there is a remainder when divided by 2
(number % 2 > 0)
//Test if a number is a multiple of x (or divisible by x with no remainder)
(number % x == 0)

Try the expressions containing the % operator below to see how they can be used to check for even or odd numbers. All even numbers are divisible (with no remainder) by 2.

public class BoolMod { public static void main(String[] args) { int age1 = 15; int age2 = 16; int divisor = 2; System.out.println("Remainder of " + age1 + "/" + divisor + " is " + (age1 % divisor) ); System.out.println("Remainder of " + age2 + "/" + divisor + " is " + (age2 % divisor) ); System.out.println("Is " + age1 + " even? " + (age1 % 2 == 0) ); System.out.println("Is " + age2 + " even? " + (age2 % 2 == 0) ); } }

The modulo operator has been used quite a bit on the AP CS A exam, so you should be familiar with it.

• Use it to check for odd or even numbers (num % 2 == 1) is odd and (num % 2 == 0) is even. Actually, you can use it to check if any number is evenly divisible by another (num1 % num2 == 0)

• Use it to get the last digit from an integer number (num % 10 = last digit on right).

• Use it to get the number of minutes left when you convert to hours (num % 60).

• Use it whenever you have limited storage and you need to wrap around to the front if the value goes over the limit (num % limit).

3.1.4. Negation !

You can use the ! operator to negate the value of a Boolean expression. When you see !, think of the word “not”.

Try to guess what the code below will print out before you run it.

public class BooleanExpressions { public static void main(String[] args) { boolean isRaining = true; boolean hasMoney = false; // Will these print true or false? System.out.println( isRaining ); System.out.println( !isRaining ); System.out.println( hasMoney ); System.out.println( !hasMoney ); System.out.println( 5 == 7 ); System.out.println( !(5 == 7) ); } }

Check your understanding

3-1-7: What is printed?

boolean isHappy = false;
System.out.println( !isHappy );

• true
• Correct. !false == true
• false
• Incorrect. !false == true

3-1-8: What is printed?

int num1 = 5;
int num2 = 10;
boolean isGt =  num1 > num2;
System.out.println( isGt );

• true
• Incorrect. 5 > 10 is false
• false
• Correct. 5 > 10 is false

3.1.5. Programming Challenge : Prime Numbers

In this activity, you will use boolean expressions to explore prime numbers. A prime number is an integer number that is only divisible by 1 and itself. For example, 3 is a prime number because it’s only divisible by 1 and 3 and no other numbers, but 4 is not a prime number because it’s divisible by 2 as well as 1 and 4.

Prime numbers are very useful in encryption algorithms because they can be used as keys for encoding and decoding. If you have the key, you can use it to divide a large number that represents something encrypted to decode it, but if you don’t have the key, it’s very hard to guess the factors of a large number to decode it. If you’re curious about this, watch this Numberphile video.

The following program checks if 5 is a prime number by seeing if it is divisible by the numbers 1 - 5. Run the code, and then answer the following questions.

1. Is 5 a prime number?

2. What boolean tests determine that a number is prime?

3. Change the number to 6 and add more boolean expressions to determine if 6 is prime. Is 6 prime?

4. Change the number to 7 and add more boolean expressions to determine if 7 is prime. Is 7 prime?

5. If you changed the boolean expressions to use <= instead of ==, would the code still help you to find prime numbers? Why or why not? Experiment and find out.

6. If you changed the boolean expressions to use >= instead of ==, would the code still help you to find prime numbers? Why or why not? Experiment and find out.

7. Are all odd numbers prime? Can you find one that is not by using boolean expressions in the code below?

8. Are all even numbers not prime? Can you find an even prime number?

Experiment with the code below changing the value of number and adding more print statements with boolean expressions to determine if the numbers 5, 6, and 7 are prime. Are all odd numbers prime? Are all even numbers not prime?

public class PrimeNumbers { public static void main(String[] args) { int number = 5; System.out.println("A prime number is only divisible by 1 and itself."); System.out.println("Is " + number + " divisible by 1 up to " + number + "?"); System.out.println("Divisible by 1? " + (number % 1 == 0)); System.out.println("Divisible by 2? " + (number % 2 == 0)); System.out.println("Divisible by 3? " + (number % 3 == 0)); System.out.println("Divisible by 4? " + (number % 4 == 0)); System.out.println("Divisible by 5? " + (number % 5 == 0)); } } ==== import static org.junit.Assert.*; import org.junit.*;; import java.io.*; public class RunestoneTests extends CodeTestHelper { @Test public void testChangedCode() { String origCode = "public class PrimeNumbers{public static void main(String[] args){int number = 5; System.out.println(\"A prime number is only divisible by 1 and itself.\"); System.out.println(\"Is \" + number + \" divisible by 1 up to \" + number + \"?\"); System.out.println(\"Divisible by 1? \" + (number % 1 == 0)); System.out.println(\"Divisible by 2? \" + (number % 2 == 0)); System.out.println(\"Divisible by 3? \" + (number % 3 == 0)); System.out.println(\"Divisible by 4? \" + (number % 4 == 0)); System.out.println(\"Divisible by 5? \" + (number % 5 == 0));}}"; boolean changed = codeChanged(origCode); assertTrue(changed); } @Test public void testBool6() throws IOException { String target = "number % 6 == 0"; boolean passed = checkCodeContains("boolean check for divisibility by 6", target); assertTrue(passed); } @Test public void testBool7() throws IOException { String target = "number % 7 == 0"; boolean passed = checkCodeContains("boolean check for divisibility by 7", target); assertTrue(passed); } }

3.1.6. Summary

• Primitive values and reference values can be compared using relational operators (i.e., == and !=) in Java.

• Arithmetic expression values can be compared using relational operators (i.e., <, >, <=, >=) in Java.

• An expression involving relational operators evaluates to a Boolean value of true or false.

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