Binary Long Division Calculator

Binary calculator: enter base-2 digits only (0 and 1) to divide in base 2.

Output: binary quotient and binary remainder.

The Binary Long Division Calculator divides one binary number by another in base 2 and shows every shift-and-subtract step. Binary long division follows the same divide–multiply–subtract–bring-down loop as decimal division, but each quotient digit can only be 0 or 1, which makes each step a simple comparison: does the divisor fit into the current bits or not. Enter two base-2 numbers to see the binary quotient, the binary remainder, and the aligned work, plus the decimal equivalents so you can check the result.

How to use the Binary Long Division Calculator

To divide binary numbers, follow these 4 steps:

Enter the binary dividend (only 0s and 1s) in the first field.
Enter the binary divisor (only 0s and 1s) in the second field.
Click Calculate to run the base-2 shift-and-subtract loop.
Read the binary quotient and remainder along with the decimal check.

Each quotient bit is 1 when the divisor fits into the current partial dividend and 0 when it does not, so the answer is built one bit at a time.

How base 2 changes division

Binary uses only the digits 0 and 1, with each place worth twice the one to its right. This simplifies division: at every step you only ask whether the divisor fits into the current bits once, because it can never fit twice — two copies would already be the next place value. So each quotient bit is a yes/no answer. The Binary Long Division Calculator uses this to reduce every step to a compare-and-subtract, which is exactly how division works inside digital hardware.

Division shares a total into equal groups. Long division does this digit by digit.

Divisor (32) — the number you divide by. Place it to the left of the bracket.

How binary long division works

The calculator produces the base-2 quotient through five internal actions:

Aligns the divisor under the leading bits of the dividend.
Writes a 1 in the quotient if the divisor fits into the current bits, otherwise a 0.
Subtracts the divisor using base-2 subtraction when a 1 is placed.
Brings down the next bit of the dividend to form the new partial value.
Repeats until every bit is used, leaving a binary remainder smaller than the divisor.

Because each quotient bit is only 0 or 1, no multiplication table is needed — every step is a single comparison and subtraction.

Aligns the divisor under the leading bits of the dividend.

Formula for binary division

The Binary Long Division Calculator uses the same identity Dividend = Divisor × Quotient + Remainder, evaluated in base 2. Each quotient bit qₖ multiplies a power of two, so the quotient equals Σ qₖ·2ᵏ. For 1010₂ ÷ 11₂, the decimal check is 10 ÷ 3 = 3 R1, so the binary answer is 11₂ R1₂.

Dividend

Divisor

Quotient

Remainder

1101 = 101 × 10 + 91 → Identity holds

Binary division example problems

These examples show base-2 shift-and-subtract with decimal checks.

Example 1 — 1010 ÷ 11 (10 ÷ 3)

11 does not fit into 1 or 10, but fits into 101; write 1 and subtract 101 − 11 = 10.
Bring down the last 0 to form 100; 11 fits once, subtract 100 − 11 = 1.
So 1010₂ ÷ 11₂ = 11₂ R1₂, matching 10 ÷ 3 = 3 R1.

Example 2 — Exact division: 1100 ÷ 100 (12 ÷ 4)

100 fits into 110 once; write 1 and subtract 110 − 100 = 10.
Bring down the last 0 to form 100; 100 fits once exactly, subtract to 0.
So 1100₂ ÷ 100₂ = 11₂ R0, matching 12 ÷ 4 = 3.

Example 3 — Divisor larger than leading bits: 1001 ÷ 10 (9 ÷ 2)

10 fits into 10 once; write 1, subtract to 0, bring down 0 to form 0.
10 does not fit into 0, write 0; bring down 1 to form 1, 10 does not fit, write 0.
So 1001₂ ÷ 10₂ = 100₂ R1₂, matching 9 ÷ 2 = 4 R1.

11 does not fit into 1 or 10, but fits into 101; write 1 and subtract 101 − 11 = 10.
Bring down the last 0 to form 100; 11 fits once, subtract 100 − 11 = 1.
So 1010₂ ÷ 11₂ = 11₂ R1₂, matching 10 ÷ 3 = 3 R1.

Worked binary problems

How do you divide 11011 by 101 in binary?

11011₂ ÷ 101₂ = 101₂ R10₂ (27 ÷ 5 = 5 R2). 101 fits into 110 once (subtract to 1), bring down 1 to form 11 — 101 does not fit, write 0; bring down 1 to form 111 — 101 fits once (subtract to 10). No bits remain, so the remainder is 10₂. Check in decimal: 5 × 5 + 2 = 27.

275

Why is each binary quotient digit only 0 or 1?

In base 2 the divisor can fit into the current bits at most once. If it fit twice, that would equal the divisor shifted left one place, which belongs to the next-higher quotient position. So every step is a single yes/no comparison, which is why binary division is just repeated shift-and-subtract.

111111

Common binary division mistakes

Binary division produces 5 frequent errors:

Writing a quotient digit larger than 1, which is impossible in base 2.
Borrowing incorrectly during base-2 subtraction.
Forgetting to write a 0 in the quotient when the divisor does not fit.
Misaligning the divisor under the wrong bits of the dividend.
Reading the remainder in decimal instead of keeping it in binary.

The Binary Long Division Calculator keeps every quotient bit as 0 or 1, aligns each subtraction, and shows the decimal equivalent for a quick check.

Writing a quotient digit larger than 1, which is impossible in base 2.

Borrowing incorrectly during base-2 subtraction.

Forgetting to write a 0 in the quotient when the divisor does not fit.

Misaligning the divisor under the wrong bits of the dividend.

Reading the remainder in decimal instead of keeping it in binary.

Frequently Asked Questions

How do you do long division in binary?

Align the divisor under the leading bits, write 1 if it fits or 0 if it does not, subtract in base 2 when you write a 1, then bring down the next bit and repeat. The result is a binary quotient and remainder.

Why can binary quotient digits only be 0 or 1?

In base 2 the divisor can fit into the current bits at most once; fitting twice would carry into the next place. So each quotient digit is a simple yes (1) or no (0).

How do I check a binary division answer?

Convert the numbers to decimal and use divisor × quotient + remainder = dividend. For 1010₂ ÷ 11₂ = 11₂ R1₂, the decimal check is 3 × 3 + 1 = 10.

How do I subtract binary numbers during division?

Subtract bit by bit, borrowing 1 from the next-higher place when needed; in binary a borrow turns a 0 into a 10 (two) before subtracting. The calculator shows each borrow.

What is the remainder in binary division?

It is the leftover bits after the last subtraction, kept in base 2 and smaller than the divisor. For 1001₂ ÷ 10₂, the remainder is 1₂.

Is binary long division the same as decimal long division?

The method is identical — divide, subtract, bring down — but base 2 makes each quotient digit a single 0/1 comparison instead of choosing from 0–9.

Does the calculator show decimal equivalents?

Yes. Alongside the binary quotient and remainder it shows the decimal values so you can verify the base-2 result quickly.

The identity in base 2

The Binary Long Division Calculator satisfies Dividend = Divisor × Quotient + Remainder evaluated in binary, where each quotient bit contributes qₖ·2ᵏ. For 11011₂ ÷ 101₂ = 101₂ R10₂, the decimal check confirms 5 × 5 + 2 = 27.