Answer to Question #204629 in Discrete Mathematics for Angelie Suarez

Question

MODULE 6:

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

1.

$F=a'b'c'+a'bc'+a'bc+ab'c'+ab'c+abc'=a'c'+ab'+a'bc+abc'$

2.

$F=a'b'c'd'+a'b'cd'+a'b'cd+a'bc'd'+a'bcd'+ab'c'd'+ab'cd'+abc'd'+$

$+abc'd+abcd'+abcd=a'b'd'+a'bd'+a'b'cd+ab'd'+abc'+abc=$

$=a'd'+a'b'cd+ab'd'+ab$

3.

$F=(a+b+c+d')(a+b+c'+d)(a+b'+c+d')(a+b'+c'+d)\times$

$\times(a+b'+c'+d')(a'+b+c'+d)(a'+b+c'+d')(a'+b'+c+d')\times$

$\times(a'+b'+c'+d')=c'(a+b)(a+b')(a'+d')$