Question

1)Find the equation for output F as a sum of minterms:

Inputs A, B, C	Output F
000	1
001	0
010	0
011	0
100	1
101	1
110	0
111	1

2)Find the equation for output F in sum of product form:

3)Find the equation for output F as a product of sums:

4

Answer 1

Ans 1)Output F in terms of sum of minterms will be: F(A,B,C)=

Ans 2)There are 2 forms of sum of products form

1) Canonical Sum of Products which is same as sum of minterms i.e.

2) Non-canonical Sum of Products: It is reduced form of sum of minterms i.e.

Ans 3) Product of sum for F will be

F = ∏ (M₁, M₂, M₃, M₆)=(A+B+C') (A+B'+C)(A+B’+C')(A’+B’+C)

The above expression is the canonical product of sum.

The non-canonical POS is:

F=(A+B+C') (A+B'+CC')(A’+B’+C) [Distributive law]

F= (A+B+C') (A+B')(A’+B’+C) [CC'=0 complementarity law]

F= (A+B'(B+C')) (A’+B’+C) [Distributive law]

F = (A+B')(A+C')(A'+B'+C) [ BB'=0 and distributive law]

F= (A+C')(B'+A(A'+C)) [Distributive law]

F= (A+B')(A+C')(B'+C) [ AA'=0 and distributive law]

F= (A+B')(A+C')(B'+C) is the non-canonical product-of-sum.