Arithmetic Operators

In the C language, mathematical operations follow specific rules that differ slightly from standard algebra, especially regarding data types and operation order. Below is a detailed compilation of notes covering Arithmetic Operators, derived directly from class examples.

1. Basic Arithmetic Operators

C provides the standard set of operators for calculation:

• + : Addition (Sum)

• - : Subtraction (Difference)

• * : Multiplication (Product)

• / : Division (Quotient)

• % : Modulus (Remainder)

While addition, subtraction, and multiplication are straightforward, Division and Modulus have special behaviour in C.

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2. The Division Operator (/)

The behaviour of the division operator depends on the data types of the operands (Int vs. Float).

Rule 1: Integer vs. Float Division

• Int / Int = Int: The result is the quotient only. The decimal part is truncated.

• Int / Float = Float: The result includes the decimal part.

Examples from Notes:

• a = 5 / 2; → Result is 2 (The 0.5 is discarded).

• a = 5.0 / 2; → Result is 2.5 (Float division).

• a = 5 / 2.0; → Result is 2.5.

Rule 2: Sign of the Quotient

For division, the sign of the result follows standard algebraic rules:

• + / + = +

• + / - = -

• - / + = -

• - / - = +

Examples:

• a = -5 / 2; → Result: -2

• a = 5 / -2; → Result: -2

• a = -5 / -2; → Result: 2

• a = 2 / -5; → Result: 0 (Since 2 < 5, quotient is 0).

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3. The Modulus Operator (%)

The modulus operator returns the remainder of the division. The notes highlight four critical rules for using %.

Rule A: The Sign Rule

The Rule: In C, the result of a modulus operation always takes the sign of the Numerator (the left operand). The sign of the denominator is ignored.

Derivation:

• Formula: Dividend = Divisor * Quotient + Remainder

Examples:

1. a = 5 % 2; → 1 (Standard positive)

2. a = 5 % -2; → 1 (Sign of 5 is +)

3. a = -5 % 2; → -1 (Sign of -5 is -)

4. a = -5 % -2; → -1 (Sign of -5 is -)

Rule B: The "Small Numerator" Rule

If the numerator is smaller than the denominator, the result is equal to the numerator itself.

Examples:

• 18 % 25 → 18

• 15 % 30 → 15

• 2 % 5 → 2

Rule C: The Float Restriction

The modulus operator is only valid for integers.

• Invalid: a = 5.0 % 2; → Compilation Error (Illegal use of floating point).

• Invalid: a = 5.0 % 2.0; → Compilation Error.

Rule D: Extracting the Unit Digit

Using modulo 10 is a standard trick to get the last digit of a number.

Examples:

• 13 % 10 → 3

• 78 % 10 → 8

• 129 % 10 → 9

Note: x % y = 0 only when x is a multiple of y.

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4. Operator Precedence and Associativity

When multiple operators appear in one expression, C uses a Priority Table to decide the order.

Priority Levels

1. High Priority: * , / , %

2. Low Priority: + , -

Associativity (The Tie-Breaker)

If operators have the same priority (e.g., * and /), they are evaluated from Left to Right (L → R).

Complex Evaluation Examples

1. Left-to-Right Evaluation (/ and *)

• Expression: a = 13 / 2 * 5;

  • Step 1: 13 / 2 = 6 (Integer division).

  • Step 2: 6 * 5 = 30.

  • Result: 30.

• Expression: a = 13 * 2 / 5;

  • Step 1: 13 * 2 = 26.

  • Step 2: 26 / 5 = 5.2 → 5 (Truncated).

  • Result: 5.

2. Multiple Divisions

• Expression: a = 21 / 5 / 2;

  • Step 1: 21 / 5 = 4.

  • Step 2: 4 / 2 = 2.

  • Result: 2.

3. Mixed Priorities

• Expression: a = 2 + 3 * 5;

  • * has higher priority.

  • Step 1: 3 * 5 = 15.

  • Step 2: 2 + 15 = 17.

  • Result: 17.

• Expression: a = 3 * 5 * 2 % 7;

  • All are high priority. Evaluate L → R.

  • 3 * 5 = 15.

  • 15 * 2 = 30.

  • 30 % 7 = 2.

  • Result: 2.

• Expression: a = 6 - 4 + 2 - 3;

  • All are low priority. Evaluate L → R.

  • 6 - 4 = 2.

  • 2 + 2 = 4.

  • 4 - 3 = 1.

  • Result: 1.

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5. Real-World Application: ATM Logic

The modulus operator is essential for checking divisibility.

Scenario: An ATM needs to check if the withdrawal amount is valid for 100-rupee notes.

• Total in Account: 8930

• Withdrawal Request: 310

Logic:

if (310 % 100 == 0) {
    // This block runs if remainder is 0
    give_money();
}
else {
    // This block runs because 310 % 100 = 10 (Not 0)
    printf("Error: Please enter cash in multiples of 100");
}

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