Binary long division: how to approach it
Binary long division works like decimal long division, but every digit is either 0 or 1. The goal is to divide one binary number by another and write the result as a binary quotient, with a possible remainder.
Method
- Write the dividend and divisor in long-division form.
- Compare from left to right: take the smallest leading part of the dividend that is at least as large as the divisor.
- Decide the quotient digit:
- write 1 if the divisor fits into that part,
- write 0 if it does not.
- Multiply and subtract using binary arithmetic.
- Bring down the next bit and repeat until all bits are used.
- Simplify the result by writing the quotient clearly, and include any remainder if one remains.
Useful checks
- Multiply the quotient by the divisor, then add the remainder. You should get the original dividend.
- If the remainder is present, it must be smaller than the divisor.
- Make sure every subtraction is done in binary, not decimal.
Tip
Keep columns aligned carefully. In binary, a small alignment mistake can change the whole result.