Answer to Question #204143 in Discrete Mathematics for Maricel

Question

Draw the logic diagram of the function and find for the

simplified Boolean expression of the following:

1. F(a, b, c) = ∑(0, 2, 3, 4, 5, 6)

2. F(a, b, c, d) = ∑(0, 2, 3, 4, 6, 8, 10, 12, 13, 14, 15)

3. F(a, b, c, d) = ∏(1, 2, 4, 5, 6, 7, 10, 11, 13, 15)

Answer 1

Solution.

1. F(a, b, c) = ∑(0, 2, 3, 4, 5, 6)

F(a,b,c)=c'+ab'+a'b.

2. F(a, b, c, d) = ∑(0, 2, 3, 4, 6, 8, 10, 12, 13, 14, 15)

F(a,b,c,d)=d'+ab+a'b'c.

3. F(a, b, c, d) = ∏(1, 2, 4, 5, 6, 7, 10, 11, 13, 15)

F(a,b,c,d)=(a+b')^(b'+d')^(a'+b+c')^(a+c'+d)^(a+c+d).