Binary Division Calculator

How it is calculated

Both numbers must be written with the digits 0 and 1 only. The tool converts each to decimal, then does integer division: q = floor(a ÷ b) and r = a mod b, so that a = b × q + r with 0 ≤ r < b. Quotient and remainder are shown in binary and in decimal. There are no fractional bits: dividing 1 by 10 (that is 1 ÷ 2) gives quotient 0 and remainder 1, not 0.1. Leading zeros and surrounding spaces are ignored. A divisor of 0 gives no result, and neither does any entry containing other characters (digits 2–9, a minus sign, a point). Each number may have at most 63 binary digits once leading zeros are removed; longer entries show no result.

Common mistakes

• Typing decimal digits such as 2 or 13. Every digit must be 0 or 1, otherwise there is no result; convert first.
• Expecting a binary fraction. Division here stops at a whole quotient, and what is left over appears as the remainder, not as digits after a point.
• Reading the remainder as part of the quotient. The remainder is always smaller than the divisor, and the quotient is only the whole number of times the divisor fits.
• Swapping dividend and divisor. The first number is divided by the second, so 11 ÷ 1101 gives quotient 0 and remainder 11.
• Entering a minus sign or a binary point (for example -101 or 1.1), or a number longer than 63 digits. Only unsigned whole binary numbers up to 63 bits are accepted.