All set, astronaut! Today, we're diving deep into Java, mastering arithmetic and logical operations on primitive types. These skills are crucial for data manipulation and decision-making during our space voyage.

Recall from our previous sessions that Java's primitive data types include int for whole numbers, float for decimal numbers, boolean for true/false values, and char for single characters. Both int and float have limitations on their numerical range, which will come into play when we discuss overflow later in this lesson.

We can perform arithmetic operations — addition (+), subtraction (-), multiplication (*), division (/), and modulus - the remainder of the division (%) — on numerical types. For example,

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1int a = 10;
2int b = 2;
3System.out.println(a + b); // Outputs: 12
4System.out.println(a - b); // Outputs: 8
5System.out.println(a * b); // Outputs: 20;
6System.out.println(a / b); // Outputs: 5
7System.out.println(a % b); // Outputs: 0

Java allows order alteration using parentheses and provides the modulus (%) operation — useful for identifying whether numbers are even or odd!

Logical operators — && (AND), || (OR), ! (NOT) — serve as decision-makers in Java and evaluate to boolean values — true or false. Here's how we can use them with two boolean values:

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1System.out.println(true && true); // true
2System.out.println(true && false); // false
3System.out.println(false && true); // false
4System.out.println(false && false); // false
5
6System.out.println(true || true); // true
7System.out.println(true || false); // true
8System.out.println(false || true); // true
9System.out.println(false || false); // false
10
11System.out.println(!true); // false
12System.out.println(!false); // true

Here, && produces true only if both boolean values are true. || delivers true if either is true. And ! reverses the boolean value.

But, of course, the main application of logical operations is for variables. Here is a quick, simple example of how they can help to make decisions:

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1int speed = 60;
2int minSpeed = 30;
3int maxSpeed = 70;
4// Check if the speed is inside the expected bounds.
5System.out.println(speed > minSpeed && speed < maxSpeed); // Prints: true

The term overflow describes what happens when we exceed the range of an integer variable. This occurs when attempting to store a value larger than what the variable's type can contain:

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1int maxInt = Integer.MAX_VALUE; // the maximal integer, equals to 2^31 - 1
2int overflow = maxInt + 1; // causes an overflow, there is no integer after the maximal one.
3System.out.println(overflow); // Prints: -2147483648, which is -2^31 - the minimal integer number

Here, maxInt is the maximum value an int can store. When we add one to it, it 'overflows' to the smallest possible integer value! This brings us to the fact that integer values are "looped" under the hood.

Well done! Today, we uncovered arithmetic operations, made complex decisions using logical operators, and understood what overflow is. On deck are practice exercises to master these essential concepts on our journey into Java. Ladies and gentlemen, it's time for launch!