Topic: Digital Electronics
Simplify the below function represented as sum of minterms
$F(A, B, C, D, E)=\Sigma(0, 1, 2, 3, 8, 9, 16, 17, 20, 21, 24, 25, 28, 29, 30, 31)$
- A. $A\overline{D}+(\overline{C+D})+\overline{A}\overline{B}\overline{C}+(\overline{\overline{A}+\overline{B}+\overline{C}})$
- B. $A\overline{D}E+(\overline{C+E})D+\overline{A}\overline{B}\overline{C}D+AE\overline{C}$
- C. $A\overline{D}B+(\overline{C+B})+\overline{C}\overline{D}\overline{E}+(\overline{B}+\overline{C}+\overline{D})$
- D. $A\overline{C}+(\overline{D+E})+\overline{A}\overline{E}+(\overline{C}+\overline{D}+\overline{E})$
Answer: A. $A\overline{D}+(\overline{C+D})+\overline{A}\overline{B}\overline{C}+(\overline{\overline{A}+\overline{B}+\overline{C}})$
Explanation: Using K-map simplification, the terms are derived as $\overline{A}\overline{B}\overline{C}+\overline{A}\overline{C}\overline{D}+A\overline{C}\overline{D}+A\overline{D}+ABC=A\overline{D}+C\overline{D}+\overline{A}\overline{B}C+ABC$, which equates equivalently to option (a).