Variables and Expressions in Java: ISC Class 11 Notes

What Variables and Expressions is about

Weightage: Variables and Expressions is topic 7 of the ISC Class XI Computer Science syllabus, in Section B - Java. CISCE weights Section B at 30 of the 70 marks in Paper I (Theory). Class XI is examined by the school, so your school sets the paper within this weightage.Source: CISCE ISC Computer Science syllabus, examination year 2028, Class XI unit weightage

Key concepts

Variables, types and named constants

A variable is a name for a memory location that holds a value of a particular type. The value can change while the program runs.

Declaration: type name; (int marks;). Initialisation: giving the first value (int marks = 87;). Java is strongly typed: a variable can hold only values compatible with its declared type, checked by the compiler.

Kinds of variables (by where they are declared): instance variables (data members of an object), class (static) variables (shared by all objects), local variables (inside methods; must be initialised before use) and parameters.

Named constants: declared with final; their value cannot change after it is assigned: final double PI = 3.14159; final int MAX_STUDENTS = 40;. Constants are written in CAPITALS by convention. Benefits: readability (GST_RATE instead of 0.18), safety (accidental change is a compile-time error) and easy maintenance (change the value in one place).

Worked example

What happens if a program contains final int LIMIT = 50; and later LIMIT = 60;? [1 mark]

Try it first, then show the solutionSolution

1. A final variable cannot be reassigned; the compiler rejects the second assignment.

Answer: A compile-time error: cannot assign a value to final variable LIMIT.

Arithmetic expressions and operators

Arithmetic operators: + (addition), − (subtraction), * (multiplication), / (division), % (remainder or modulus).

• Integer division drops the fraction: 17 / 5 = 3.
• % gives the remainder: 17 % 5 = 2; its sign follows the left operand: −17 % 5 = −2.
• + also joins strings: 3 + 4 + "Java" = "7Java" (left to right: 3 + 4 first), but "Java" + 3 + 4 = "Java34".

Unary operators: unary minus (−x), increment ++ and decrement −−.

• Prefix (++a): change first, then use the new value.
• Postfix (a++): use the current value, then change.

Compound assignment: +=, −=, *=, /=, %= (x += y means x = x + y, with an automatic cast to x's type).

Writing formulas as Java expressions: simple interest = p * r * t / 100; area of triangle = 0.5 * b * h; average of three = (a + b + c) / 3.0 (use 3.0 for a decimal result); distance = Math.sqrt(x * x + y * y).

Worked example

If x = 5, find x and y after int y = x++ * 2 + --x;. [2 marks]

Try it first, then show the solutionSolution

1. x++ gives 5 (x becomes 6); 5 × 2 = 10.
2. --x makes x 5 and gives 5; y = 10 + 5 = 15.

Answer: x = 5, y = 15.

Relational and logical expressions

Relational operators compare values and give a boolean: < , <= , > , >= , == (equal to), != (not equal to).

Logical operators combine boolean values:

Operator	Meaning	True when
&&	AND	both operands are true
\	\		OR	at least one is true
!	NOT	the operand is false

Short-circuit evaluation: && does not evaluate its right operand if the left is false; || does not evaluate its right operand if the left is true. This prevents errors such as division by zero: (z != 0) && (10 / z > 1) is safe when z is 0.

Common logical expressions: even number: n % 2 == 0; leap year: (y % 4 == 0 && y % 100 != 0) || y % 400 == 0; within range 10 to 20: n >= 10 && n <= 20; vowel test: ch == 'a' || ch == 'e' || ...

= vs ==: = assigns; == compares. if (a = 5) does not compile in Java for an int a, which helps catch the mistake.

Worked example

Evaluate !(4 > 2 || 1 > 5) && true. [1 mark]

Try it first, then show the solutionSolution

1. 4 > 2 is true, so the OR is true; ! gives false; false && true = false.

Answer: false.

Precedence and associativity

Precedence decides which operator applies first; associativity decides the order among operators of the same precedence.

Level (high to low)	Operators	Associativity
1	postfix a++ a−−	left to right
2	prefix ++a −−a, unary − +, !, (type) cast	right to left
3	* / %	left to right
4	+ −	left to right
5	< <= > >=	left to right
6	== !=	left to right
7	&&	left to right
8	\	\		left to right
9	?: (ternary)	right to left
10	= += −= *= /= %=	right to left

Brackets override precedence. Use them to make intent clear.

The program below evaluates several expressions; note the left-to-right associativity of − and /, and the effect of prefix and postfix increment.

// Precedence, associativity, increment operators and short-circuit evaluation.
public class Operators
{
    public static void main(String[] args)
    {
        System.out.println("2 + 3 * 4     = " + (2 + 3 * 4));        // * before +
        System.out.println("(2 + 3) * 4   = " + ((2 + 3) * 4));
        System.out.println("20 - 6 - 4    = " + (20 - 6 - 4));       // left to right
        System.out.println("100 / 10 / 5  = " + (100 / 10 / 5));
        System.out.println("17 % 5 * 2    = " + (17 % 5 * 2));
        System.out.println("-17 % 5       = " + (-17 % 5));          // sign follows the left operand

        int a = 5;
        int b = a++ + ++a;          // 5 (then a = 6) + 7 (a becomes 7 first)
        System.out.println("a = " + a + ", b = " + b);

        int x = 10, y = 3;
        x += y;                     // x = 13
        x *= 2;                     // x = 26
        x %= 7;                     // x = 5
        System.out.println("x = " + x);

        int p = 4;
        int q = p--;                // q gets 4, then p becomes 3
        System.out.println("p = " + p + ", q = " + q);

        int z = 0;
        boolean safe = (z != 0) && (10 / z > 1);   // second part never runs: no division by zero
        System.out.println("safe = " + safe);

        int i = 2, j = 9;
        System.out.println(i < j && j % i == 1 || !(i == 2));
        int k = 1;
        k = k++ + k;                // 1 + 2
        System.out.println("k = " + k);
    }
}

Output:

2 + 3 * 4     = 14
(2 + 3) * 4   = 20
20 - 6 - 4    = 10
100 / 10 / 5  = 2
17 % 5 * 2    = 4
-17 % 5       = -2
a = 7, b = 12
x = 5
p = 3, q = 4
safe = false
true
k = 3

In b = a++ + ++a with a = 5: a++ gives 5 (a becomes 6), then ++a makes a 7 and gives 7, so b = 12.

Worked example

Evaluate 8 / 3 * 3 + 8 % 3 and 20 − 6 − 4. [2 marks]

Try it first, then show the solutionSolution

1. 8 / 3 = 2 (int); 2 × 3 = 6; 8 % 3 = 2; 6 + 2 = 8.
2. Left to right: (20 − 6) − 4 = 10, not 20 − (6 − 4) = 18.

Answer: 8 and 10.

Assignment: left-hand side and right-hand side

The assignment variable = expression; works in two steps:

1. The right-hand side (RHS) is evaluated to a value (an r-value).
2. The value is stored in the location named by the left-hand side (LHS), which must be a variable (an l-value), not a constant or an expression.

So x = x + 1; is meaningful: the RHS uses the old value of x; the LHS names the location to update. 5 = x; and a + b = c; are errors because the LHS is not a storage location.

Type compatibility: the RHS type must be assignable to the LHS type (widening is automatic; narrowing needs a cast).

Chained assignment is right-associative: a = b = c = 0; sets c, then b, then a.

Swapping two values needs a temporary variable (or arithmetic): t = p; p = q; q = t;.

Worked example

After int p = 6, q = 4; p = p + q; q = p − q; p = p − q;, what are p and q? [2 marks]

Try it first, then show the solutionSolution

1. p = 10; q = 10 − 4 = 6; p = 10 − 6 = 4.
2. The values have been swapped without a temporary variable.

Answer: p = 4, q = 6.

Variables denoting objects are references; library functions

A variable of a class type holds a reference to an object, not the object itself.

• int n = m; copies the value; changing n does not change m.
• References r2 = r1; copies the reference: r1 and r2 now name the same object (aliasing); a change through r2 is seen through r1.
• r1 == r2 compares references (same object?), not contents.

// Variables that denote objects hold references: two variables can refer to the same object.
public class References
{
    int count;

    References(int c)
    {
        count = c;
    }

    public static void main(String[] args)
    {
        int m = 10;
        int n = m;           // copies the value
        n = n + 5;
        System.out.println("m = " + m + ", n = " + n);

        References r1 = new References(10);
        References r2 = r1;  // copies the reference: both name the SAME object
        r2.count = r2.count + 5;
        System.out.println("r1.count = " + r1.count + ", r2.count = " + r2.count);
        System.out.println("r1 == r2 ? " + (r1 == r2));

        References r3 = new References(15);
        System.out.println("r1 == r3 ? " + (r1 == r3) + " (same value, different objects)");

        final double GST_RATE = 0.18;   // named constant: cannot be reassigned
        double price = 500;
        System.out.println("price with GST = " + (price + price * GST_RATE));
    }
}

Output:

m = 10, n = 15
r1.count = 15, r2.count = 15
r1 == r2 ? true
r1 == r3 ? false (same value, different objects)
price with GST = 590.0

Library functions (java.lang.Math, no import needed): Math.sqrt(x), Math.pow(a, b), Math.abs(x), Math.max(a, b), Math.min(a, b), Math.round(x), Math.ceil(x), Math.floor(x), Math.cbrt(x), Math.random(), Math.PI. They make formulas short and accurate.

// Library functions in expressions: roots of ax^2 + bx + c = 0 using Math.sqrt,
// and a few other Math methods.
public class Quadratic
{
    static void roots(double a, double b, double c)
    {
        double d = b * b - 4 * a * c;                  // discriminant
        if (d >= 0)
        {
            double r1 = (-b + Math.sqrt(d)) / (2 * a);
            double r2 = (-b - Math.sqrt(d)) / (2 * a);
            System.out.println("a=" + a + " b=" + b + " c=" + c + ": roots " + r1 + " and " + r2);
        }
        else
            System.out.println("a=" + a + " b=" + b + " c=" + c + ": no real roots (d = " + d + ")");
    }

    public static void main(String[] args)
    {
        roots(1, -5, 6);
        roots(2, 4, -6);
        roots(1, 2, 5);
        System.out.println("Math.pow(2, 10) = " + Math.pow(2, 10));
        System.out.println("Math.abs(-7.5) = " + Math.abs(-7.5));
        System.out.println("Math.max(12, 19) = " + Math.max(12, 19));
        System.out.println("Math.ceil(4.1) = " + Math.ceil(4.1) + ", Math.floor(4.9) = " + Math.floor(4.9));
        System.out.println("Math.round(-2.5) = " + Math.round(-2.5));
        double r = 7;
        System.out.println("area of circle r=7: " + Math.round(Math.PI * r * r * 100) / 100.0);
    }
}

Output:

a=1.0 b=-5.0 c=6.0: roots 3.0 and 2.0
a=2.0 b=4.0 c=-6.0: roots 1.0 and -3.0
a=1.0 b=2.0 c=5.0: no real roots (d = -16.0)
Math.pow(2, 10) = 1024.0
Math.abs(-7.5) = 7.5
Math.max(12, 19) = 19
Math.ceil(4.1) = 5.0, Math.floor(4.9) = 4.0
Math.round(-2.5) = -2
area of circle r=7: 153.94

Worked example

Write a Java expression for the hypotenuse of a right triangle with sides a and b, and evaluate it for a = 3, b = 4. [1 mark]

Try it first, then show the solutionSolution

1. Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2)) = √25 = 5.0.

Answer: Math.sqrt(a * a + b * b) (or with Math.pow) gives 5.0.

Variables and Expressions in real life

Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Topics in this chapter

• Relational and Logical Expressions, Object References and Library Functions
• Variables, Constants, Arithmetic Operators, Increment and Decrement, and Precedence

Variables and Expressions: syntax and key facts

Integer division and remainder

a = (a / b) * b + a % b (for ints)

17 = 3 × 5 + 2.

Increment

Prefix ++a: change then use; postfix a++: use then change

Compound assignment

x op= y means x = (type of x) (x op y)

Common Java formulas

SI = p * r * t / 100; average = (a + b + c) / 3.0; root = (-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a)

Precedence (short)

postfix > prefix, unary, ! > * / % > + - > relational > == != > && > || > ?: > assignment

Variables and Expressions: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Variables and Expressions

The question patterns to expect, and the method that works for each.

Tricks to remember Variables and Expressions

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Please My Dear Aunt Sally... in Java: U-M-A-R-E-L-A

  Unary, Multiplicative, Additive, Relational, Equality, Logical (&& then ||), Assignment.

  Use it when: Precedence order.

• Pre-change, post-use

  ++a changes before use; a++ uses before change.

  Use it when: Increment operators.

• RHS first, LHS last

  Compute the right side completely, then store it on the left.

  Use it when: Assignment.

• Strings are sticky

  Once a String appears in a + chain (left to right), everything after it is joined as text.

  Use it when: String concatenation.

Variables and Expressions: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section D style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 5-mark question split into 2 + 1 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Variables and Expressions

The slips examiners see most often, and what to write instead.

• ✗Mistake: Writing -b + Math.sqrt(d) / 2 * a

  Without brackets, / and * apply before +, and / 2 * a multiplies by a instead of dividing.

  ✓Do this: (-b + Math.sqrt(d)) / (2 * a).

  Usually costs: 1-2 marks.

• ✗Mistake: Using = for comparison

  = assigns; == compares.

  ✓Do this: In conditions, use == (or equals for Strings).

  Usually costs: 1 mark.

• ✗Mistake: Forgetting integer division in averages

  (a + b + c) / 3 drops the fraction when all are ints.

  ✓Do this: Divide by 3.0.

  Usually costs: 1 mark.

• ✗Mistake: Thinking r2 = r1 copies the object

  It copies only the reference; both refer to one object.

  ✓Do this: Create a new object if a separate copy is needed.

  Usually costs: 1 mark.

Practice questions on Variables and Expressions

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   Which operator has the highest precedence?
   (a) &&
   (b) *
   (c) ==
   (d) =

   Hint

   Multiplicative beats relational and logical.

   Answer

   (b) *.

2. Q2 · 1 mark · Very short answerExam level

   What is a named constant in Java?

   Hint

   final.

   Answer

   A variable declared with final, whose value cannot be changed once assigned (for example final double PI = 3.14159;).

3. Q3 · 2 marks · Short answerExam level

   Evaluate: (i) int a = 8, b = 3; a / b * b + a % b; (ii) char c = 'A'; c += 5; (iii) double d = 15 / 4 + 15 % 4 / 2.0;

   Hint

   Integer division where both are ints.

   Answer

   (i) 8; (ii) c = 'F'; (iii) 3 + 3 / 2.0 = 3 + 1.5 = 4.5.

4. Q4 · 2 marks · Short answerHarder exam level

   Explain the difference between the LHS and RHS of an assignment with x = x * 2 + 1;.

   Hint

   Value vs location.

   Answer

   The RHS is an expression evaluated using the current value of x (if x is 4, x * 2 + 1 = 9). The LHS must be a variable (an l-value) naming the location where the result is stored, so x becomes 9. The same name means 'value' on the right and 'location' on the left.

5. Q5 · 2 marks · Short answerHarder exam level

   Write a Java expression to check that a character ch is a vowel (lower case), and one to check that year y is a leap year.

   Hint

   || chains; leap rule.

   Answer

   ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u'; (y % 4 == 0 && y % 100 != 0) || y % 400 == 0.

6. Q6 · 2 marks · Short answerHarder exam level

   Give the output: int m = 10; m -= 3 * 2; System.out.println(m); System.out.println(Math.cbrt(27) + " " + Math.min(-3, -7));

   Hint

   Compound assignment evaluates the RHS first.

   Answer

   4 (m = 10 − 6), then '3.0 -7'.

7. Q7 · 5 marks · Short answerHOTS / competency

   Suppose class Box has a field int w. After Box b1 = new Box(); b1.w = 5; Box b2 = b1; b2.w = 9; Box b3 = new Box(); b3.w = 9;, what are b1.w, b1 == b2 and b2 == b3? Explain.

   Hint

   References.

   Answer

   b1.w = 9, because b2 refers to the same object as b1 and changed it. b1 == b2 is true (same object). b2 == b3 is false: b3 is a different object, even though its w is also 9; == compares references, not contents.

8. Q8 · 2 marks · Short answerHOTS / competency

   Write a program segment to convert a temperature t in Fahrenheit to Celsius rounded to one decimal place, and give the result for t = 100.

   Hint

   (F − 32) × 5 / 9.

   Answer

   double c = (t - 32) * 5 / 9.0; c = Math.round(c * 10) / 10.0; For t = 100: (68 × 5) / 9 = 37.777... → 37.8.

9. Q9 · 5 marks · Short answerHOTS / competency

   Rewrite with brackets to show the order of evaluation and find the value: 2 + 3 * 4 - 6 / 2 % 4 + 7.

   Hint

   *, /, % left to right before + and −.

   Answer

   ((2 + (3 * 4)) − ((6 / 2) % 4)) + 7 = (2 + 12) − (3 % 4) + 7 = 14 − 3 + 7 = 18.

10. Q10 · 10 marks · Long answerHOTS / competency

    Write a class Interest with final double RATE = 8.5; a method double compound(double p, int years) using Math.pow, and main() printing the compound amount for p = 50,000 over 3 years (rounded to two decimals).

    Hint

    A = p(1 + r/100)ⁿ.

    Answer

    class Interest { static final double RATE = 8.5; static double compound(double p, int years) { return p * Math.pow(1 + RATE / 100, years); } public static void main(String[] args) { double a = compound(50000, 3); System.out.println(Math.round(a * 100) / 100.0); } } A = 50,000 × 1.085³ = 50,000 × 1.277289125 = 63,864.46.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Keyword for a named constant?Show answer

   final.

2. 2.17 % 5?Show answer

   2.

3. 3.Prefix vs postfix ++?Show answer

   Prefix changes then uses; postfix uses then changes.

4. 4.Associativity of = ?Show answer

   Right to left.

5. 5.What does r2 = r1 copy for objects?Show answer

   The reference, not the object.

6. 6.Does && always evaluate both sides?Show answer

   No; it stops if the left side is false.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Variable = named typed storage; final = constant.
• ☐/ with ints truncates; % gives the remainder (sign of left operand).
• ☐++a: change then use; a++: use then change.
• ☐&&, || short-circuit; = assigns, == compares.
• ☐Precedence: unary > * / % > + − > relational > equality > && > || > ?: > assignment.
• ☐Object variables are references; Math.sqrt, pow, abs, max, min, round, ceil, floor.

Variables and Expressions: frequently asked questions