Topic: Digital Electronics
Simplify Boolean function represented in sum of product of min-terms,
$F(x,y,z)=\Sigma(0,2,4,5,6)$
- A. $z'+xy'$
- B. $x'y'z'+xyz+xy'z'$
- C. $xyz+x'+y'+z'$
- D. $xy+yz+zx$
Answer: A. $z'+xy'$
Explanation: Using a 3-variable K-map:
Minterms 0, 2, 4, 6 form a quad, which simplifies to $\overline{z}$.
Minterms 4 and 5 form a pair, which simplifies to $x\overline{y}$.
Therefore, the simplified function is $F = \overline{z} + x\overline{y}$ (or $z'+xy'$).