Computer Science
Find the complement of the following expressions:
(a) (A + B).(B + C).(A + C)
(b) A.B + (A'.B').(B.C + B'.C')
Boolean Algebra
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Answer
(a) (A + B).(B + C).(A + C)
Complement of (A + B).(B + C).(A + C)
= [(A + B).(B + C).(A + C)]'
= (A + B)' + [(B + C).(A + C)]'
= (A + B)' + (B + C)' + (A + C)'
= A'.B' + B'.C' + A'.C'
(b) A.B + (A'.B').(B.C + B'.C')
Complement of A.B + (A'.B').(B.C + B'.C')
= [A.B + (A'.B').(B.C + B'.C')]'
= (A.B)'.[(A'.B').(B.C + B'.C')]'
= (A' + B').[(A'.B')' + (B.C + B'.C')']
= (A' + B').[A + B + [(B.C)' . (B'.C')']]
= (A' + B').[A + B + [(B' + C').(B + C)]]
= (A' + B').[A + B + [BB' + B'C + BC' + CC']]
= (A' + B').[A + B + [0 + B'C + BC' + 0]]
= (A' + B').(A + B + B'C + BC')
= (A' + B').(A + B'C + B(1 + C'))
= (A' + B').(A + B + B'C)
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