Q. A function πΉ(π΄, π΅, πΆ) defined by three Boolean variables A, B and C when expressed as sum of products is given by
πΉ = π΄Μ β π΅Μ β πΆΜ + π΄Μ β π΅ β πΆΜ + π΄ β π΅Μ β πΆΜ
where, π΄Μ , π΅Μ , and πΆΜ are the complements of the respective variables. The product of sums (POS) form of the function F is
(A) πΉ = (π΄ + π΅ + πΆ) β (π΄ + π΅Μ + πΆ) β (π΄Μ + π΅ + πΆ)
(B) πΉ = (π΄Μ + π΅Μ + πΆΜ ) β (π΄Μ + π΅ + πΆΜ ) β (π΄ + π΅Μ + πΆΜ )
(C) πΉ = (π΄ + π΅ + πΆΜ ) β (π΄ + π΅Μ + πΆΜ ) β (π΄Μ + π΅ + πΆΜ ) β (π΄Μ + π΅Μ + πΆ) β (π΄Μ + π΅Μ + πΆΜ )
(D) πΉ = (π΄Μ + π΅Μ + πΆ) β (π΄Μ + π΅ + πΆ) β (π΄ + π΅Μ + πΆ) β (π΄ + π΅ + πΆΜ ) β (π΄ + π΅ + πΆ)
Ans: F = (A + B + CΜ ) . (A + BΜ + CΜ ) . (AΜ + B + CΜ ) . (AΜ + BΜ + C) . (AΜ + BΜ + CΜ )
Sol:
F = AΜ .BΜ .CΜ + AΜ .B.CΜ + A.BΜ .CΜ
In terms of minterms, this can be represented as:
F = βmΒ (0, 2, 4)
The equivalent maxterm will contain the terms not present in the minterm representation, i.e.
F =Β βm (0, 2, 4) = Ο(1, 3, 5, 6, 7) = M1. M3. M5. M6. M7
β (A + B + CΜ ) (A + BΜ + CΜ ) (AΜ + B + CΜ ) (AΜ + BΜ + C) (AΜ + BΜ + CΜ )