Binary Division Calculator
Type two binary numbers and the quotient and remainder appear instantly as you type — no Calculate button; the result updates on every keystroke, in every base. The long-division method is explained below.
Divide Binary Numbers
Full binary calculator (all operations) → · Binary multiplication calculator →
How to divide binary numbers
- Set up a long division. The first number is the dividend (what gets divided), the second is the divisor.
- Take bits from the left until the divisor fits. Compare lengths first, then values: a longer bit string is always the bigger number.
- Write 1 in the quotient and subtract the divisor. If the divisor does not fit, write 0 instead and move on.
- Bring down the next bit and repeat. Keep going until every bit of the dividend has been brought down.
- What remains is the remainder. It must be smaller than the divisor — if it is not, a step went wrong.
Worked example: 1010₂ ÷ 11₂ = 11₂ remainder 1
| Step | Partial dividend | Does 11 fit? | Quotient bit | Subtract | Remainder so far |
|---|---|---|---|---|---|
| 1 | 10 (first two bits) | No — 10 is less than 11 | — | — | 10 |
| 2 | 101 (bring down the next 1) | Yes, once | 1 | 101 − 11 = 10 | 10 |
| 3 | 100 (bring down the last 0) | Yes, once | 1 | 100 − 11 = 1 | 1 |
The quotient bits are 11 and the final remainder is 1. Check by multiplying back: 11 × 11 = 1001, plus the remainder 1 gives 1010 — the original dividend. In decimal: 10 ÷ 3 = 3 remainder 1.
Common mistakes in binary division
Forgetting the 0 quotient bits. When the divisor does not fit at some step, that step still earns a 0 in the quotient. Skipping it shifts every later bit and wrecks the answer. Trusting a remainder that is too big: a remainder must always be smaller than the divisor — if yours is not, the divisor actually fit one more time. And the evergreen: dividing by zero, which is undefined in binary just as in decimal; the calculator above will refuse it outright.
Frequently asked questions
How do I divide binary numbers?
Use long division, the same as in decimal. Take bits of the dividend from the left until the divisor fits, write a 1 in the quotient, subtract the divisor, and bring down the next bit. When the divisor does not fit, write a 0 and bring down the next bit instead. What is left over at the end is the remainder. The calculator above gives the quotient and remainder live as you type.
What is 1010 ÷ 11 in binary?
1010 ÷ 11 = 11 remainder 1 in binary. In decimal: 10 ÷ 3 = 3 remainder 1 — and binary 11 is 3. The remainder (1) is always smaller than the divisor (11, i.e. 3), which is how you know the division is finished.
What are the binary division rules?
There are no division tables in binary — only two decisions per step: does the divisor fit into the current partial dividend? If yes, the quotient bit is 1 and you subtract; if no, the quotient bit is 0 and you bring down the next bit. Dividing by zero is never allowed.
How do I check a binary division?
Multiply back: quotient × divisor + remainder must equal the original dividend. For 1010 ÷ 11 = 11 remainder 1: 11 × 11 = 1001, plus remainder 1 gives 1010. If the check fails, the division went wrong — usually a subtraction step.
How do I divide binary numbers in Python?
Use int(a, 2) // int(b, 2) for the quotient and int(a, 2) % int(b, 2) for the remainder, then bin() to convert back. Example: bin(int("1010", 2) // int("11", 2))[2:] gives "11", and the remainder expression gives "1".