Binary calculator

Add, subtract, multiply, or divide two binary numbers and read the answer in binary, decimal, and hex. Enter values in binary, decimal, or 0x hex. For addition the tool also shows the column-by-column carries, the exact carry chain a row of full adders produces. For example, 1011 + 0110 = 10001 (that is 11 + 6 = 17).

How to use it

Type a number into A and B, then pick an operation. Bare strings of 0s and 1s are read as binary; include a digit from 2 to 9 for a decimal value, or prefix with 0x for hex, so you can mix forms freely. The result appears in all three bases, and division also reports a quotient and remainder. Addition adds a small table showing the carry into each column above the two operands and the sum.

Adding binary by hand

Binary addition follows the same rule as decimal: add each column from the right and carry when a column overflows. The only difference is that a binary column overflows at 2 instead of 10, so 1 + 1 = 10 (write 0, carry 1). Working 1011 + 0110: the columns produce carries that ripple left three times before the final carry lands the leading 1, giving 10001. That rippling carry is exactly why a simple adder is called a ripple-carry adder.

This is what an adder does in gates

The carry row this tool shows is not a metaphor: each column is a full adder, a small circuit that takes one bit of A, one bit of B, and the carry from the column to its right, and outputs a sum bit plus the carry into the next column. Chain eight of them and you can add two bytes in one shot, which is the arithmetic core of every CPU. Subtraction reuses the same adder by adding the two's complement of the second number. Build one in the lab and watch the carries light up.

Frequently asked

How do you add binary numbers?

Add column by column from the right, carrying whenever a column reaches 2, since 1 + 1 = 10 in binary (write 0, carry 1). For 1011 + 0110 the carry ripples through three columns to give 10001, which is 17.

What is 1011 plus 0110 in binary?

1011 (11) plus 0110 (6) equals 10001, which is 17 in decimal.

How do you subtract binary numbers?

You can borrow column by column, but hardware adds the two's complement of the second number so one adder handles both. This tool shows the plain signed result and its decimal value.

Are the carries the same as in a full adder?

Yes. The carry row shown for addition is exactly the carry chain a row of full adders produces, each adding one bit of A, one bit of B, and the carry from the previous column.