Question

1. Simplify the following expressions using Boolean algebra.

a.A+AB

b.AB+AB'

c.A'BC+AC

d.A'B+ABC'+ABC

Answer 1

a.A+AB = A(1+B)

=A.1                (Since by identity law 1+B=1)

=A                   (By A * 1 = A )

b.AB+AB' =A(B+B’)

=A.1                   (By complement law, B+B’=1)

=A                      (By A * 1 = A )

c.A'BC+AC =C(A’B+A)

=C(A + A')(A + B) (By AND Distributive Law ,A + (B.C)=(A + B).(A + C))
=C(A+B)                                        (By complement law, A+A’=1)

d.A'B+ABC'+ABC =A’B+AB(C+C’)

=A’B+AB                     (By complement law, C+C’=1)

=B(A+A’)

=B                              (By complement law, A+A’=1)