Integer Arithmetic Calculator

Calculator Input Panel

Calculation Result and Steps

Enter your values above and press Calculate to see detailed steps.

Example Integer Arithmetic Table

Use this sample dataset to understand how the operations behave on integers.

Worked Example: Using the Integer Arithmetic Calculator

Scenario: You want to analyze the numbers 84 and 36.

1. Select Binary operation mode.
2. Enter A = 84 and B = 36.
3. Choose GCD(A, B) from the operation list.
4. Click Calculate.

The calculator shows stepwise Euclidean algorithm and returns GCD = 12.

Now switch operation to LCM(A, B) using the same inputs and calculate again.

You obtain LCM = 252, confirming: 84 × 36 = 12 × 252.

Follow similar steps with other modes to validate work or debug algorithms.

What This Integer Arithmetic Calculator Offers

This tool centralizes essential integer operations into one interactive interface.

• Instant evaluation of simple, advanced, and number-theoretic expressions.
• Transparent step-by-step output suitable for teaching and documentation.
• Error handling for invalid input, division by zero, and malformed expressions.

Core Integer Operations Covered

The calculator supports core arithmetic, structure analysis, and bit-level logic:

• Basic: addition, subtraction, multiplication, integer division, modulo, powers.
• Number theory: GCD, LCM, coprimality check, extended GCD coefficients.
• Bitwise: AND, OR, XOR, left/right shifts for binary manipulation tasks.

Practical Use Cases for Integer Arithmetic

Use this calculator wherever precise integer logic is required:

• Teaching divisibility, modular arithmetic, and discrete mathematics concepts.
• Checking steps in homework, competitive programming, and coding interviews.
• Designing algorithms, encryption preliminaries, checksum logic, and validation rules.

Formulas Used in Integer Arithmetic

• Addition: R = A + B
• Subtraction: R = A - B
• Multiplication: R = A × B
• Integer Division: A = B × q + r, where 0 ≤ r < |B|, q = intdiv(A, B)
• Modulo: R = A mod B = r
• Power: R = A^B (B ≥ 0)
• GCD: iterative GCD(A,B) = GCD(B, A mod B)
• LCM: LCM(A,B) = |A×B| / GCD(A,B) (A,B ≠ 0)
• Bitwise: AND, OR, XOR applied on binary representations of integers.
• Shifts: A << B = A × 2^B, A >> B = floor(A / 2^B)
• Extended GCD: finds x,y with a×x + b×y = gcd(a,b)
• Sequence average (floor): floor(Σ nᵢ / count)
• Range span: max(sequence) - min(sequence)

All computations follow deterministic integer rules suitable for rigorous verification.

How to Use This Calculator

1. Select a mode: Binary, Expression, or Sequence.
2. Enter integers or expressions according to the chosen mode.
3. Pick the desired operation from the dropdown list.
4. Click Calculate to view result and stepwise breakdown.
5. Use Download CSV or Download PDF to export results.

Designed as a compact integer lab for educators, students, and professionals.