Question

Simplify the following expressions using Boolean algebra.

a. AB + A(CD + CD’)

b. (BC’ + A’D) (AB’ + CD’)

Answer 1

1) AB + A(CD + CD')
= AB +AC(D + D')         Taking C common
= AB + AC(1)                 Since, D + D' = 1
= AB + AC
= A(B + C)                    Taking A common

2) (BC' + A'D)(AB' + CD')
= AB'BC + BC'CD' + A'DAB' + A'DCD'        Expanding the brackets
= A(0)C + B(0)D' + (0)DB' + AC(0)                Since, A.A' =B.B' = C.C' = D.D' = 0
= 0   <---- ANSWER

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