How to convert following Karnaugh map to a simplified Boolean expression?
It cannot be further simplified with a Karnaugh map, but with a little Boolean algebra:
\$F = \bar A \bar B \bar C + A \bar B C + \bar A B C + A B \bar C\$
\$F = \bar A( \bar B \bar C + B C) + A (\bar B C + B \bar C)\$
\$F = \bar A . \overline {(B \oplus C)} + A . (B \oplus C)\$
let \$(B \oplus C) = X\$
\$F = \bar A \bar X + A X\$
\$F = \overline {(A \oplus X)}\$
now substituting X:
\$F = \overline { (A \oplus B \oplus C) }\$