F = ∑m(4,5,7,8,10,14,15,16,17,18,21,22,23,29,31) ∑m(1,2,12,13)
F = [tex]\bar{A} B D \bar{E}+\bar{A} B \bar{C} \bar{E}+\bar{A} \bar{B} C \bar{D}[/tex] + [tex]A \ C E+A \bar{B} D \bar{E}+A \bar{B} \bar{C} \bar{D}[/tex] + [tex]\bar{B} C E+C D E[/tex]
Explanation:
Given data:
F(A,B,C,D,E) = π M (0,3,6,9,11,19,20,24,25,26,27,28,30) π D ( 1,2,12,13 )
The terms given here are maximum so it is called as max terms.
F = ∑m(4,5,7,8,10,14,15,16,17,18,21,22,23,29,31) ∑m(1,2,12,13)
The terms given here are minimum so it is called as min terms.
n = variables = 5
Size of K- map = [tex]2^{n}[/tex]
Size of K- map = [tex]2^{5}[/tex]
Size of K- map = 32
For A = 0
The table attached below for A=0, from the sequence of table [tex]F_{1}[/tex] is calculated.
[tex]F_{1}[/tex] = [tex]\bar{A} B D \bar{E}+\bar{A} B \bar{C} \bar{E}+\bar{A} \bar{B} C \bar{D}[/tex]
For A = 1
The table attached below for A=1, from the sequence of table [tex]F_{2}[/tex] is calculated.
[tex]F_{2}=A C E+A \bar{B} D \bar{E}+A \bar{B} \bar{C} \bar{D}[/tex]
From the sequence of table [tex]F_{3}[/tex] is calculated.
[tex]F_{3}[/tex] = [tex]\bar{B} C E+C D E[/tex]
The final expression are calculated.
F = [tex]F_{1}[/tex] + [tex]F_{2}[/tex] + [tex]F_{3}[/tex]
F = [tex]\bar{A} B D \bar{E}+\bar{A} B \bar{C} \bar{E}+\bar{A} \bar{B} C \bar{D}[/tex] + [tex]A \ C E+A \bar{B} D \bar{E}+A \bar{B} \bar{C} \bar{D}[/tex] + [tex]\bar{B} C E+C D E[/tex]
