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Binary Division Calculator

Divide two binary numbers using long division. Shows the quotient and remainder in binary and decimal.

By Christopher FloiedPublished Updated

Can't be 0

Results

Quotient (Binary)

101

Remainder (Binary)

1

Quotient (Decimal)

5

Remainder (Decimal)

1

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Binary Division Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.

2

Review your inputs

Double-check that all values are correct and match the units or format shown for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Binary Division Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Binary Division Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

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Synthetic Division Calculator

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Binary Calculator (All Operations)

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About Binary Division Calculator

Binary division uses the same long division algorithm as decimal, but each step is simpler because the trial quotient digit is either 0 or 1 — either the divisor fits into the current partial remainder or it does not. At each step, shift down the next bit of the dividend, compare the partial remainder with the divisor: if the partial remainder is greater or equal, write 1 in the quotient and subtract the divisor; otherwise write 0. Continue until all bits have been processed. The algorithm produces an integer quotient and a remainder. Binary division is used in processors, modular arithmetic, CRC computation, and cryptographic algorithms.

The Math Behind It

Binary long division proceeds bit by bit from the MSB of the dividend. Initialize partial remainder R = 0. For each bit dᵢ of the dividend (MSB first): shift R left by 1 and set R[0] = dᵢ. If R ≥ divisor, set quotient bit = 1 and R = R − divisor; else set quotient bit = 0. After processing all bits, R is the remainder. This is the restoring division algorithm. Non-restoring division avoids the subtraction when R < divisor by allowing R to go negative and correcting later. SRT division (used in modern CPUs) produces multiple quotient bits per cycle. Division by powers of 2 is simply a right shift.

Formula Reference

Binary Long Division

A ÷ B = Q remainder R, where A = B × Q + R

Variables: A = dividend, B = divisor, Q = quotient, R = remainder

Worked Examples

Example 1: Divide 11010₂ ÷ 101₂

Divide 11010 (26) by 101 (5).

Step 1:Process bits left to right: 1, 11, 110 ≥ 101 → quotient 1, remainder 1
Step 2:Bring down 1: 11 < 101 → quotient 0
Step 3:Bring down 0: 110 ≥ 101 → quotient 1, remainder 1

11010₂ ÷ 101₂ = 101₂ remainder 1₂ (26 ÷ 5 = 5 remainder 1)

Common Mistakes & Tips

  • !Starting from the LSB instead of the MSB — binary long division proceeds from left to right.
  • !Forgetting the remainder — integer division truncates, and the remainder must be tracked.
  • !Division by zero — undefined in binary just as in decimal.

Related Concepts

Binary Multiplication

The inverse of division.

Binary Calculator

All four arithmetic operations in binary.

Frequently Asked Questions

How do modern CPUs divide?

Modern CPUs use SRT (Sweeney, Robertson, Tocher) division or Newton-Raphson iterative methods to compute multiple quotient bits per clock cycle.

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