Math
Binary Division Calculator
Enter a binary dividend and divisor.
The calculator performs binary long division bit by bit, drawing the tableau with each subtraction, and reports the quotient and remainder. Set fraction bits to continue the division past the binary point.
Digits 0 and 1 only. A leading minus sign is allowed; spaces or underscores can group bits (1011 0110).
Digits 0 and 1 only.
0 shows an integer quotient with remainder. Use 4-8 to continue the long division past the binary point.
Try an example
Result
Binary result
—
- Decimal check
- —
- Hexadecimal
- —
- Octal
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the binary division calculator solves
Binary long division works like decimal long division but each quotient digit is only ever 0 or 1: either the divisor fits into the current working value or it does not. This page brings the dividend bits down one at a time, subtracts when the divisor fits, and shows the remainder at the end.
The long-division steps
- Start with an empty working value and bring down the leftmost bit of the dividend.
- If the working value is at least the divisor, write 1 in the quotient and subtract the divisor; otherwise write 0.
- Bring down the next bit and repeat until the dividend is used up.
- What is left is the remainder. To get fraction bits, keep bringing down zeros past the binary point.
How to use it
- Enter the dividend (the number being divided) and the divisor.
- Leave fraction bits at 0 for an integer quotient with remainder, or set it to 4-8 to see the quotient as a binary fraction.
- Read the tableau: each subtraction line is the divisor aligned under the current working value, and the line below it is what remains.
- Confirm with the decimal check: divisor × quotient + remainder should equal the dividend.
How to read the answer
The result is written as quotient R remainder, both in binary. With fraction bits the quotient continues after a binary point; a trailing ellipsis means the fraction does not terminate within the requested bits. A division that comes out even has remainder 0.
Common mistakes and edge cases
- Division by zero is undefined; the calculator reports an error instead of a result.
- Comparing the working value with the divisor by digit count alone: 100 is larger than 11 even though both have a leading 1; compare the full values.
- Forgetting to write a 0 in the quotient when the divisor does not fit. Every brought-down bit produces a quotient bit.
- Fraction bits are truncated, not rounded; 1 ÷ 11 = 0.0101… never ends, like 1/3 in decimal.
- A negative sign on either input makes the quotient negative; the remainder keeps the sign of the dividend.
Worked examples
Division with remainder
100010 ÷ 11
Binary result
1011 R 1
Exact division
110100 ÷ 100
Binary result
1101 R 0
Dividend smaller than divisor
11 ÷ 101
Binary result
0 R 11
Fraction bits
1 ÷ 100 with 4 fraction bits
Binary result
0 R 1
Negative dividend
−100010 ÷ 11
Binary result
-1011 R -1
Division by zero
1010 ÷ 0
Binary result
—
Frequently asked questions
How do you divide binary numbers?+
Use long division. Bring down one bit at a time; if the divisor fits into the working value, write 1 in the quotient and subtract, otherwise write 0. Whatever is left at the end is the remainder.
What does R mean?+
R stands for remainder. 100010 ÷ 11 = 1011 R 1 means the divisor goes in 1011 times with 1 left over: 11 × 1011 + 1 = 100010.
How do I get a decimal-style answer instead of a remainder?+
Set fraction bits above 0. The calculator keeps bringing down zeros past the binary point, giving a quotient like 1011.0101. Some fractions repeat forever, just as 1/3 does in decimal.
Why is dividing by 10 (binary) a shift?+
Binary 10 is two. Dividing by two moves every bit one place to the right; the bit that falls off is the remainder. Dividing by 100 shifts two places, and so on.
What happens if the dividend is smaller than the divisor?+
The quotient is 0 and the remainder is the whole dividend. Turn on fraction bits to see the value as a binary fraction less than 1.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Binary Calculator
Add, subtract, multiply, or divide binary numbers with the column method shown: carries, borrows, partial products, and a long-division tableau, plus decimal, hex, and octal equivalents.
Binary Multiplication Calculator
Multiply binary numbers with every shifted partial product listed in an aligned grid, then the final sum, plus the product in decimal, hex, and octal.
Binary Subtraction Calculator
Subtract binary numbers with each borrow shown in an aligned column grid, negative answers handled, and the difference checked in decimal, hex, and octal.
Bit Shift Calculator
Left, logical right, and arithmetic right shifts at 4 to 64 bits with the before/after bit rows, bits shifted out, overflow detection, and the ×2^n or ÷2^n meaning of the shift.
Binary Fraction Converter
Convert decimal fractions (or ratios like 1/3) to binary with repeating-block detection, or binary fractions back to exact decimals, with the multiply-by-2 table and place-value table shown.
Decimal to Binary Converter
Convert decimal to binary with the repeated-division steps, fractional parts by repeated multiplication (0.625 → 0.101), repeating-fraction detection, and negatives as a sign or two's complement.
Last updated: September 4, 2026