Binary Division Calculator
This calculator divides one binary number by another using the same long division method you'd use in decimal, but restricted to the two digits 0 and 1. It's useful for computer science students, programmers and anyone working with binary arithmetic who wants to check a division by hand or see exactly how a binary quotient and remainder are derived, since binary division is also the basis of the shift-and-subtract circuits used in computer processors. You enter a dividend and a divisor as strings of 0s and 1s (up to 32 bits each), or choose one of five example presets to see how the tool behaves with different numbers. The calculator instantly returns the quotient and remainder in both binary and decimal, the full binary and decimal expressions side by side, and a verification check confirming that divisor multiplied by quotient plus remainder equals the original dividend. Below the results sits a complete step-by-step table showing, for every bit of the dividend, the partial remainder, whether the divisor fits, the resulting quotient bit, and the value left after subtraction, so you can follow the working line by line rather than just reading off an answer. Only digits 0 and 1 are accepted, and the divisor cannot be zero; the tool will flag either problem with an on-screen error message before it will calculate.
1. Dividend (Number to Divide)
2. Divisor (Divide By)
Full Expression
Verification
Step-by-Step Long Division Working
How Binary Division Works
Binary division follows exactly the same long division procedure as decimal division, but the only digits available are 0 and 1. Because of this restriction, the only question at each step is whether the divisor fits into the current partial remainder: if the partial remainder is greater than or equal to the divisor, the answer is 1 (and the divisor is subtracted); if not, the answer is 0 (and nothing is subtracted).
The Binary Long Division Algorithm
- Write the dividend and divisor in binary.
- Start with the leftmost bit of the dividend. Bring down bits one at a time until the partial remainder is greater than or equal to the divisor.
- If the partial remainder is greater than or equal to the divisor, write 1 in the quotient position and subtract the divisor from the partial remainder.
- If the partial remainder is less than the divisor, write 0 in the quotient position and bring down the next bit without subtracting.
- Continue until all bits of the dividend have been processed.
- The value remaining at the end is the remainder.
Worked Example: 1101 divided by 10
Dividend: 1101 (decimal 13). Divisor: 10 (decimal 2).
| Step | Partial Remainder | Divisor fits? | Quotient bit | After subtraction |
|---|---|---|---|---|
| Bring down 1 | 1 | No (1 < 10) | 0 | 1 |
| Bring down 1 | 11 | Yes (11 ≥ 10) | 1 | 11 - 10 = 1 |
| Bring down 0 | 10 | Yes (10 ≥ 10) | 1 | 10 - 10 = 0 |
| Bring down 1 | 01 | No (1 < 10) | 0 | 1 |
Quotient: 0110 = 110 (decimal 6). Remainder: 1 (decimal 1). Verification: 10 x 110 + 1 = 1100 + 1 = 1101. Correct.
Binary vs Decimal Division
In decimal division you ask "how many times does the divisor fit (0 to 9)?" In binary division you only ask "does it fit once or not at all (0 or 1)?" This simplicity makes binary division straightforward to implement in digital hardware using shift-and-subtract circuits, which is the basis for division operations in all modern processors.
Remainders in Binary Division
The remainder is always strictly less than the divisor, just as in decimal division. If the dividend is exactly divisible by the divisor, the remainder is 0. You can verify any binary division result by checking: Divisor x Quotient + Remainder = Dividend. Both operations (multiplication and addition) can be performed in binary to confirm the result.
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Method: Binary long division (restoring division algorithm). Each step determines one quotient bit by comparing the partial remainder against the divisor and subtracting when the divisor fits. Results verified by computing Divisor x Quotient + Remainder and confirming it equals the Dividend.
This calculator performs exact integer binary division. Fractional binary division (binary fixed-point) is not covered here. Inputs are limited to 32-bit unsigned integers.