Binary Division Calculator

Binary division follows the exact same logical framework as traditional long division in base-10, but restricted strictly to the digits 0 and 1. To divide a dividend by a divisor, you compare the divisor to the leftmost bits of the dividend. If the divisor fits, you record a 1 in the quotient and subtract the divisor from those bits. If it does not fit, you record a 0, bring down the next bit, and repeat the process until all bits have been processed. The final value left over after the last subtraction step serves as the binary remainder.

Let us walk through dividing the binary number 1101 (decimal 13) by 11 (decimal 3). First, examine the leftmost digits of the dividend (11) against the divisor (11). Since 11 equals 11, it fits 1 time. We write 1 in the quotient and subtract 11 from 11, leaving a remainder of 0. Next, bring down the 0 from 1101, making it 0. Since the divisor 11 cannot go into 0, we add a 0 to the quotient. Finally, bring down the last digit 1 to form 01. Because 11 still cannot fit into 1, we add another 0 to the quotient and keep 1 as our final remainder. Thus, dividing 1101 by 11 yields a quotient of 100 with a remainder of 1.

Always align your binary places carefully when performing manual checks to avoid shifting errors. Remember that dividing by zero in binary is undefined, exactly as it is in standard decimal arithmetic. If you need to handle fractional results or negative numbers, convert your inputs into signed two's complement representations before computing.