1. What is Modulus Operation?

The modulus operation finds the remainder after division of one number by another. In mathematics, the result is always non-negative and less than the divisor.

2. How Does Modulus Calculation Work?

The calculator uses the modulus formula:

Where:

• \( a \) — Dividend (the number being divided)
• \( b \) — Divisor (the number dividing by)
• \( \left\lfloor x \right\rfloor \) — Floor function (greatest integer less than or equal to x)

Explanation: The formula subtracts the product of divisor and the integer division result from the dividend to get the remainder.

3. Importance of Modulus

Details: Modulus operations are fundamental in computer science (hashing, cryptography), engineering (signal processing), and mathematics (number theory). They're used for cyclic operations and checking divisibility.

4. Using the Calculator

Tips: Enter any real number for dividend and any non-zero real number for divisor. The calculator will compute the non-negative remainder.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between modulus and remainder?
A: For positive numbers they're the same, but modulus always returns a non-negative result, while remainder can be negative.

Q2: Can modulus be calculated for decimal numbers?
A: Yes, this calculator works with both integers and decimals.

Q3: What happens if divisor is zero?
A: Division by zero is undefined, so the calculator requires a non-zero divisor.

Q4: Why is modulus important in programming?
A: It's used for array indexing, circular buffers, determining even/odd numbers, and many algorithms.

Q5: Can modulus be negative?
A: The result is always non-negative (0 ≤ result < divisor) in mathematical modulus operations.