Perform addition, subtraction, multiplication, and division on binary numbers with step-by-step visualization.
In binary there are only two digits, so a column that sums to 2 does not write '2': it writes 0 and carries 1. This tool performs addition, subtraction, multiplication, and division on two binary numbers and lays the work out as you would write it by hand, with carries shown above the columns, borrows marked in subtraction, partial products stacked in multiplication, and quotient and remainder given for division. Results are displayed in binary, and the thing users most often trip on is that every digit entered is read in base 2: '10' means two, not ten.
A concrete input and expected output from the current implementation.
Input
1011 + 1101
Expected output
1111 (carries) 1011 + 1101 ------- 11000
Worked right to left: 1 + 1 writes 0 and carries 1, and that carry keeps propagating, so each of the next three columns also writes 0 and carries; the final 1 + 1 + carry writes 1 and produces the leftover carry that becomes the leading bit. In decimal the same sum is 11 + 13 = 24, and 11000 is 16 + 8.
Addition works right to left: each column adds its two digits plus the incoming carry, writes the low bit, and passes 1 onward when the sum reaches 2. A leftover carry becomes a new leading bit. Subtraction borrows from the nearest 1-bit leftward. Multiplication stacks one partial product per multiplier bit and sums them with shifts. Division is binary long division, subtracting shifted divisors to build the quotient.
Each operand is a string of 0 and 1 characters; any other digit is rejected. Operands of different lengths align by their least significant bits, and leading zeros are ignored. The step view renders each column's intermediate state: a carry row above an addition, marked borrows in a subtraction, stacked partial products, and the running quotient and remainder in a division.
Because binary has no digit 2. The rightmost column sums to 2, so it writes 0 and carries 1; the carry cascades through the remaining columns, each writing 0 and carrying, and the final carry becomes a new leftmost bit. So 111 + 1 = 1000, which is 7 + 1 = 8 in decimal. The carry row in the step view shows this propagation.
No. The tool reads every character as a base-2 digit, so it is designed for binary input only; convert decimal values yourself first. Ten becomes 1010, so a decimal 10 + 10 becomes 1010 + 1010 = 10100, which is 20. If your entries contain digits 2-9, that is a sign the values were written in decimal by mistake.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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