Binary Arithmetic is like regular arithmetic, but using binary rather than decimal numbers. In most computers, it is done with a fixed word size, with an extra bit to handle carry-over for exceeding it. See also BooleanLogic.
BinaryArithmetic is an example where simplification makes something very easy: Multiplication in decimal requires memorizing the times table, but in binary it is basically a copy. Example:
100101 * 101001 = 37 * 41
--------------- -------
100101 148 (37*4=120+28)
000000 37 (37*1)
100101 ----
000000 1 <- carry
000000 1517
100101
---------------
1 <- carry
10111101101 = 1517