Question

Express the complement of each of the following functions in two forms 1). sum of minterms and 2). product of maxterms; (The results can be expressed with index numbers)

a) F(A,B,C,D) = Σ(0,1,2,5,9).

b). G(A,B,C,D)= П(0,1,5,8,10)

Answer 1

a) Given Function is

F (A, B, C, D) = ​ m (0, 1, 2, 5, 9)

The complement of the above Function is nothing but all the minterms other than the above minterms

So the complement of F is F' in  sum of minterms form is

F' (A, B, C, D) = ​ m (3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15)

The complement of the above Function is nothing but all the maxterms other than the given minterms

So the complement of F is F' in  sum of maxterms form is

F' (A, B, C, D) = ​ M (3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15)

b) Given Function is

G (A, B, C, D) = ​ M (0, 1, 5, 8, 10)

The complement of the above Function is nothing but all the maxterms other than the given maxterms

So the complement of F is F' in  sum of maxterms form is

G' (A, B, C, D) = ​ M (2, 3, 4, 6, 7, 9, 11, 12, 13, 14, 15)

The complement of the above Function is nothing but all the minterms other than the given maxterms

So the complement of F is F' in  sum of minterms form is

G' (A, B, C, D) = ​ m (2, 3, 4, 6, 7, 9, 11, 12, 13, 14, 15)