Binary Division Calculator
Enter two binary numbers (using only 0s and 1s) to divide them. The calculator returns the quotient and remainder in both binary and decimal, and walks through every step of the long-division process so you can follow the working.
Formula
Worked example
Divide 1101(2) by 10(2). In decimal this is 13 / 2. Bring down bits one at a time: 1 < 10 (write 0), 11 >= 10 (write 1, subtract: 11-10=1), 10 >= 10 (write 1, subtract: 10-10=0), 01 < 10 (write 0, remainder 1). Quotient = 0110(2) = 6(10), remainder = 1(2) = 1(10). Check: 6x2+1=13.
How binary division works
Binary division follows exactly the same long-division algorithm taught in school arithmetic, but with only two possible digits (0 and 1) instead of ten. At each step you bring down the next bit of the dividend and ask a single yes/no question: is the current partial dividend greater than or equal to the divisor? If yes, the next quotient bit is 1 and you subtract the divisor from the partial dividend. If no, the quotient bit is 0 and the partial dividend carries forward unchanged. Repeating this for every bit of the dividend produces the full quotient, and whatever value remains after the last step is the remainder. Because the only question is "fits or does not fit", no multiplication table is needed, which is one reason binary arithmetic is so well-suited to digital electronics.
Division by powers of 2 and bit shifting
When the divisor is a power of 2 (1, 10, 100, 1000 in binary, which are 1, 2, 4, 8 in decimal), binary division is equivalent to a right bit-shift. Dividing by 10(2) shifts all bits one place to the right; dividing by 100(2) shifts two places. This is far faster in hardware and software than a full division circuit. The bits that fall off the right end of the word form the remainder. For example, 1101(2) right-shifted by 1 gives 110(2) with a remainder of 1(2), matching 13/2 = 6 remainder 1. Many compilers automatically replace division-by-constant-power-of-2 with a shift instruction to exploit this.
Quotient and remainder in digital systems
In computing, integer division always produces two values: the quotient (how many whole times the divisor fits into the dividend) and the remainder (what is left over). In most programming languages the quotient is the floor of the true ratio and the remainder is always non-negative for positive operands. Binary division is used in virtually every digital system: from dividing a CPU clock frequency to derive a slower peripheral clock, to computing memory addresses, to implementing modular arithmetic for checksums and cryptographic operations. Understanding the manual long-division method helps programmers reason about overflow, precision, and signed-vs-unsigned behavior.
Signed binary division and two's complement
This calculator works with unsigned (non-negative) binary integers. In real processors, signed integers are usually represented in two's complement form. Dividing signed numbers requires extra steps: detect the signs of both operands, perform unsigned division on their magnitudes, and apply the sign rule (positive quotient if signs match, negative if they differ). The remainder takes the sign of the dividend. Most hardware divide instructions handle this internally, but awareness of signed representation is important when debugging low-level code or working with fixed-width registers.
Binary division quick reference
| Dividend (bin) | Divisor (bin) | Quotient (bin) | Remainder (bin) | Decimal check |
|---|---|---|---|---|
| 0 | 1 | 0 | 0 | 0 / 1 = 0 |
| 1 | 1 | 1 | 0 | 1 / 1 = 1 |
| 10 | 1 | 10 | 0 | 2 / 1 = 2 |
| 10 | 10 | 1 | 0 | 2 / 2 = 1 |
| 11 | 10 | 1 | 1 | 3 / 2 = 1 r 1 |
| 100 | 10 | 10 | 0 | 4 / 2 = 2 |
| 101 | 10 | 10 | 1 | 5 / 2 = 2 r 1 |
| 110 | 11 | 10 | 0 | 6 / 3 = 2 |
| 111 | 11 | 10 | 1 | 7 / 3 = 2 r 1 |
| 1010 | 10 | 101 | 0 | 10 / 2 = 5 |
| 1100 | 100 | 11 | 0 | 12 / 4 = 3 |
| 1111 | 11 | 101 | 0 | 15 / 3 = 5 |
Common single-bit and small binary division results.
Frequently asked questions
How do I divide binary numbers by hand?
Use long division. Write the dividend across the top. Working left to right, bring down one bit at a time to form a partial dividend. If the partial dividend is greater than or equal to the divisor, write 1 in the quotient and subtract the divisor. If it is less, write 0 and carry the partial dividend forward. Repeat for every bit. The leftover value after the final bit is the remainder. The step-by-step panel on this calculator shows every stage with your actual inputs.
What is the remainder in binary division?
The remainder is the amount left over after dividing as many whole times as possible. For example, 1101 (13) divided by 11 (3) goes 4 times (100 in binary) with 1 left over, because 4 x 3 = 12 and 13 - 12 = 1. A remainder of zero means the dividend is exactly divisible by the divisor.
Can I divide binary numbers with a remainder?
Yes. Binary division behaves exactly like decimal integer division. The result has a quotient part and a remainder part. If you need a fractional binary result, you would continue the long division process past the binary point, writing additional bits after a binary point in the quotient, but this calculator focuses on integer (quotient + remainder) division.
Why does dividing by a power of 2 equal a right bit shift?
In binary, each position represents a power of 2. Shifting all bits one place to the right is the same as dividing each bit's positional value by 2, which divides the entire number by 2. Shifting right by two places divides by 4, and so on. Bits shifted off the right end form the remainder. This is why CPUs use shift instructions as a fast substitute for division by 2, 4, 8, etc.
How do I convert a binary number to decimal before dividing?
Multiply each bit by its place value (starting from the right: 1, 2, 4, 8, 16, ...) and sum the results. For example, 1101 = 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1 = 13. This calculator shows the decimal equivalents of your dividend, divisor, quotient, and remainder automatically so you can verify the result.