Binary calculator

Type a binary sum: `1011 + 110`, `1011 - 110`, `101 * 11` or `1100 / 11`. The answer appears in binary, hex and decimal, and Show the steps does it the paper way, with the carries, borrows and partial products written out.

Spaces and the _ character inside a number are ignored, so `1010_1010` is fine. The same box does `AND`, `OR`, `XOR`, `NOT` and shifts, which line the bits up in the working.

There are only four facts to know. 0 + 0 is 0, 0 + 1 is 1, 1 + 1 is 10 (write 0, carry 1), and 1 + 1 + 1 is 11 (write 1, carry 1). Add from the right, column by column, and carry into the next column whenever a column reaches 2.

`1011 + 110` is 11 + 6 in decimal. From the right: 1 + 0 is 1; 1 + 1 is 10, carry 1; 0 + 1 + 1 is 10, carry 1; 1 + 0 + 1 is 10, carry 1; and the last carry comes down. That gives 10001, which is 17.

Subtraction borrows 2 from the next column when it needs to take 1 from 0. The working marks every borrow. If the second number is the bigger one, the answer is negative.

Binary multiplication is the easiest kind of long multiplication there is. Each digit of the bottom number is 0 or 1, so each row is either nothing or a copy of the top number shifted left. Add the copies and you're done: `101 × 11` is 101 plus 1010, which is 1111. A computer's multiplier does the same thing in hardware.

In November 1937 George Stibitz, a researcher at Bell Labs, finished a binary adder built from telephone relays at home. He later called it the Model K, after the kitchen table it was said to have been put together on. The rules it wired into relays are the four in the section above, and every adder in every processor since follows them.