Question

The minimized form of the logical expression $(\overline{A}\overline{B}\overline{C}+\overline{A}B\overline{C}+\overline{A}BC+AB\overline{C})$ is

Answer 1

$Y=\overline{A}\overline{B}\overline{C}+\overline{A}B\overline{C}+\overline{A}BC+AB\overline{C}$
$=\overline{A}\overline{C}(B+\overline{B})+\overline{A}BC+AB\overline{C}$
$=\overline{A}(\overline{C}+BC)+AB\overline{C}$
$=\overline{A}(C+\overline{C})(\overline{C}+B)+AB\overline{C}$
$=\overline{A}\overline{C}+\overline{A}B+AB\overline{C}=\overline{A}\overline{C}+B(\overline{A}+A\overline{C})$
$=\overline{A}\overline{C}+B(A+\overline{A})(\overline{A}+\overline{C})=\overline{A}\overline{C}+\overline{A}B+B\overline{C}$