How binary arithmetic works
Binary arithmetic follows the same rules as decimal arithmetic but uses only two digits, 0 and 1. When the sum of a column reaches 2 you write 0 and carry 1 to the next column, just as you carry when a decimal column reaches 10.
Subtraction borrows from the next higher bit when the minuend digit is smaller than the subtrahend digit. Multiplication and division follow the same long-hand algorithms taught in decimal, but with a much smaller multiplication table.
1 + 1 = 10 (binary)
One plus one equals two, written as 10 in base 2.