Binary Division Calculator
Divide one binary number by another and see every long division step.
Updated
Binary Division Calculator
Our Binary Division Calculator divides one binary number (the dividend) by another (the divisor) and gives the quotient and remainder in binary and decimal. It shows the long division one step at a time, so you can follow or check the working, and gives the exact quotient as a binary fraction, with repeating bits marked.
Quick answer
Divide binary numbers with long division: bring down one bit at a time and, if the divisor fits, write 1 and subtract it; otherwise write 0. What is left at the end is the remainder. For example, 1110 ÷ 11 = 100 remainder 10, which is 14 ÷ 3 = 4 remainder 2. Enter any two binary numbers above and the calculator shows the quotient, remainder and every step instantly.
- Quotient bits are only 0 or 1: just ask “does the divisor fit?”
- Check it: quotient × divisor + remainder = dividend
- Dividing by 2: shift right one place; the bit that drops off is the remainder
- Fractions: 1 ÷ 11 = 0.(01), with the bits in brackets repeating forever
Binary Long Division
Binary division works exactly like decimal long division, but each quotient digit is either 0 or 1, so there is no trial and error:
- Bring down the next bit of the dividend, starting from the left.
- If the current value is at least the divisor, write 1 in the quotient and subtract the divisor.
- If it is smaller, write 0 in the quotient and keep the value as it is.
- Repeat until every bit has been brought down. The value left over is the remainder.
Worked Example
1110 ÷ 11 (14 ÷ 3), one row per bit of the dividend:
| Step | Bring down | Current | ≥ 11? | Quotient bit | Remainder |
|---|---|---|---|---|---|
| 1 | 1 | 1 | No | 0 | 1 |
| 2 | 1 | 11 | Yes: 11 − 11 = 0 | 1 | 0 |
| 3 | 1 | 1 | No | 0 | 1 |
| 4 | 0 | 10 | No | 0 | 10 |
Reading the quotient bits top to bottom gives 0100 = 100 (4), and the last remainder is 10 (2). Check: 100 × 11 + 10 = 1100 + 10 = 1110.
Example Calculations
| Binary | Decimal |
|---|---|
| 1110 ÷ 11 = 100 R 10 | 14 ÷ 3 = 4 R 2 |
| 1100 ÷ 11 = 100 | 12 ÷ 3 = 4 |
| 101010 ÷ 110 = 111 | 42 ÷ 6 = 7 |
| 11011 ÷ 101 = 101 R 10 | 27 ÷ 5 = 5 R 2 |
| 11111111 ÷ 1111 = 10001 | 255 ÷ 15 = 17 |
| 1100100 ÷ 111 = 1110 R 10 | 100 ÷ 7 = 14 R 2 |
Dividing by Powers of Two
Dividing by 10 (2) in binary is like dividing by 10 in decimal: every digit moves one place to the right. The bits that fall off the end are the remainder. So 1101 ÷ 10 = 110 R 1 (13 ÷ 2 = 6 R 1), and 1101 ÷ 100 = 11 R 1 (13 ÷ 4 = 3 R 1). Computers use this right shift as a fast way to divide by 2, 4, 8 and so on.
Binary Fractions
If you keep dividing after the last bit by bringing down 0s, you get the digits after the binary point. Each place is worth half the one before: 0.1 is ½, 0.01 is ¼, 0.001 is ⅛.
1111 ÷ 100 = 11.11 (15 ÷ 4 = 3.75)
1 ÷ 11 = 0.(01) (1 ÷ 3 = 0.333…)
1 ÷ 101 = 0.(0011) (1 ÷ 5 = 0.2)
1 ÷ 1010 = 0.0(0011) (1 ÷ 10 = 0.1)
Bits in brackets repeat forever. A fraction ends in binary only when its denominator (in lowest terms) is a power of 2, which is why 0.1 and 0.2 can’t be stored exactly by a computer.
Key Terms
- Dividend
- The number being divided.
- Divisor
- The number you divide by. It can’t be 0.
- Quotient
- How many whole times the divisor fits into the dividend.
- Remainder
- What is left over; always smaller than the divisor.
- Binary point
- The binary version of the decimal point; places after it are worth ½, ¼, ⅛ and so on.
How to Use the Binary Division Calculator
- Enter the dividend. Type the binary number being divided in the “Dividend (binary)” box, for example 1110. Spaces, underscores and a 0b prefix are ignored. Pressing Enter moves you to the next box.
- Enter the divisor. Type the binary number you are dividing by in the “Divisor (binary)” box, for example 11. It can’t be 0.
- Read the quotient and remainder. The quotient appears as soon as both numbers are filled, with the remainder and the decimal working underneath (for example 1110 ÷ 11 = 100 R 10, 14 ÷ 3 = 4 R 2).
- Follow the steps. Below the result, a table shows each long division step: the bit brought down, whether the divisor fits, the quotient bit and the new remainder. A second table gives the quotient and remainder in binary and decimal, and the exact quotient as a binary fraction.
- Copy the result. Press Copy to copy the binary quotient. Press Clear or Esc to start again.
Example: enter 11011 and 101 and the result is 101 remainder 10 (27 ÷ 5 = 5 remainder 2), with the exact quotient 101.(0110).
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you divide binary numbers?
Use long division, just like in decimal but simpler. Bring down the dividend’s bits one at a time from the left. Each time, check whether the divisor fits into the current value: if it does, write 1 in the quotient and subtract the divisor; if not, write 0. When all bits are used, what is left is the remainder. For example, 1110 ÷ 11 = 100 remainder 10 (14 ÷ 3 = 4 remainder 2).
Why is binary long division easier than decimal?
Each quotient digit can only be 0 or 1, so there is no guessing how many times the divisor fits. You only ask “does it fit or not?” and then either subtract the divisor once or not at all.
How do you find the remainder in binary division?
It is the value left over after the last step of long division, and it is always smaller than the divisor. For 11011 ÷ 101 (27 ÷ 5), the quotient is 101 (5) and the remainder is 10 (2). Check: 101 × 101 + 10 = 11011, because 5 × 5 + 2 = 27.
How do you divide a binary number by 2?
Shift every bit one place to the right. The bit that drops off the end is the remainder: 1101 ÷ 10 = 110 remainder 1 (13 ÷ 2 = 6 remainder 1). Dividing by 4 (100) shifts two places, by 8 (1000) three places, and so on. The Bit Shift Calculator does this directly.
Can binary division give a fraction?
Yes. Keep dividing past the binary point by bringing down 0s. 101 ÷ 10 = 10.1 (2.5) and 1111 ÷ 100 = 11.11 (3.75) end cleanly, but 1 ÷ 11 = 0.010101… (1 ÷ 3) repeats forever. The calculator shows the exact quotient with the repeating bits in brackets, such as 0.(01).
Why can’t 0.1 be written exactly in binary?
Because 1 ÷ 10 in binary is 1 ÷ 1010 = 0.0(0011), with 0011 repeating forever. Only fractions whose denominator is a power of 2, such as 1/2, 1/4 or 3/8, end in binary. That is why computers store 0.1 as a close approximation and why 0.1 + 0.2 is not exactly 0.3 in most programming languages.
What happens if you divide by 0 in binary?
It is undefined, exactly as in decimal: no number multiplied by 0 gives back a non-zero dividend. The calculator shows a message instead of a result.
What if the dividend is smaller than the divisor?
Then the divisor never fits, every quotient bit is 0, and the quotient is 0 with the whole dividend as the remainder. For example, 10 ÷ 101 = 0 remainder 10 (2 ÷ 5 = 0 remainder 2). As a fraction it is 0.(0110).
Is the Binary Division Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Binary Division Calculator to divide any two binary numbers instantly.