Binary Division Calculator — Divide Binary Numbers
Enter a binary dividend and a binary divisor to find the integer quotient and remainder. Results appear in both binary and decimal with a step-by-step verification.
Binary: 111 • Remainder: 0 (0₂)
Dividend (N)
Divisor (D)
Quotient Q = ⌊N / D⌋
Remainder R = N − Q × D
Verify: N = Q × D + R
- 1
Dividend N in decimal
21 - 2
Divisor D in decimal
3 - 3
Remainder R = N mod D
21 mod 3 = 0 - 4
Quotient Q = ⌊N ÷ D⌋
21 ÷ 3 = 7Integer division — the remainder is discarded from the quotient.
How does this calculator work?
Dividing binary number N by D gives an integer quotient Q = ⌊N/D⌋ and remainder R = N − Q×D, satisfying N = Q×D + R with 0 ≤ R < D. Enter a binary dividend and divisor above to see the quotient and remainder in binary and decimal, plus a verification that Q×D+R equals N.
Formula
How this is calculated
Binary integer division produces two results: a quotient Q (how many times D goes into N completely) and a remainder R (what is left over). The relationship N = Q × D + R always holds, with 0 ≤ R < D. This is identical to decimal integer division — the only difference is that binary numbers are expressed in base 2.
The algorithm used internally is the same restoring-division or non-restoring-division approach implemented in digital hardware: at each step, try subtracting the (shifted) divisor from the running partial remainder; if the subtraction is non-negative, the quotient bit is 1 and the result becomes the new partial remainder; if negative, the quotient bit is 0 and the original partial remainder is kept. Repeating for every bit of the quotient gives the final answer.
This calculator performs the division with JavaScript BigInt for exact arbitrary-precision results. It shows quotient and remainder in both binary and decimal, and verifies the identity N = Q × D + R.
Frequently asked questions
The remainder is the amount left over after dividing as many complete groups of D as possible from N. In binary it is a non-negative integer strictly less than the divisor. For example, 10101₂ (21) ÷ 011₂ (3) gives quotient 7 and remainder 0, since 21 = 7 × 3 + 0.
The procedure is the same — estimate how many times the divisor fits, subtract, bring down the next bit — but because each digit is 0 or 1, the "estimate" at each step is always either 0 or 1. This makes binary long division simpler than decimal in some ways, though the steps are more numerous for large values.
No. Division by zero is undefined in mathematics and in all computer arithmetic; the calculator rejects a zero divisor and asks for a non-zero value.
Also known as
TG we-Calculate Editorial Team. (2026). Binary Division Calculator — Divide Binary Numbers [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/binary-division-calculator
TG we-Calculate Editorial Team. "Binary Division Calculator — Divide Binary Numbers." TG we-Calculate. 2026. https://we-calculate.com/calculator/binary-division-calculator.
TG we-Calculate Editorial Team, "Binary Division Calculator — Divide Binary Numbers," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/binary-division-calculator
@misc{wecalculate_binary_division_calculator, title = {Binary Division Calculator — Divide Binary Numbers}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/binary-division-calculator}}, year = {2026}, note = {TG we-Calculate} }
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