Using Table 1-2, derive the Boolean expression for the S (sum) output of the full-adder in sum-of-products form. Then by algebraic manipulation show that S can be expressed as the exclusive-OR of the three input variables. 

S = x ⊕ y ⊕ z

Table 1-2

TABLE 1-1 Basic Identities of Boolean Algebra (2) x 0 = 0 (4) x 1 = x (1) x + 0 = x (3) x + 1 = 1 (5) x + x = x (7) x + x = 1 (9) x + y = y + x (11) x + (y + 2) = (x + y) + z (13) x(y + z) = xy + xz (15) (x + y)' = x'y' (17) (x')' = x (6) x.x = x (8) x x = 0 (10) xy = yx (12) x(yz) = (xy)z = (14) x+yx= (16) (xy)' = x + y' (x + y)(x + 2)