ALU or Arithmetic Logical Unit is a digital circuit to do arithmetic operations like addition, subtraction, division, multiplication and logical operations like and, or, xor, nand, nor etc. A simple block diagram of a 4 bit ALU for operations and,or,xor and Add is shown here :

The circuit functionality of a 1 bit ALU is shown here, depending upon the control signal S1 and S0 the circuit operates as follows:

for Control signal S1 = 0 , S0 = 0, the output is A And B,

for Control signal S1 = 0 , S0 = 1, the output is A Or B,

for Control signal S1 = 1 , S0 = 0, the output is A Xor B,

for Control signal S1 = 1 , S0 = 1, the output is A Add B..