Topic: Digital Circuits
Simplify the Boolean expression: $F(w,x,y,z)=\Sigma(0,1,2,4,5,6,8,9,12,13,14)$
- A. $w+x+y+z$
- B. $y'+w'z'+xz'$
- C. $y+w'z'+xz$
- D. $x+z'w'y+x'$
Answer: B. $y'+w'z'+xz'$
Explanation: Plotting the minterms on a 4-variable K-map:
Minterms 0,1,4,5,8,9,12,13 can be grouped together into a block of 8 cells. This eliminates $w, x,$ and $z$, leaving $y'$.
Minterms 2 and 6 group with 0 and 4 to form a block of 4, yielding $w'z'$.
Minterms 14 and 6 group with 12 and 4 to form a block of 4, yielding $xz'$.
Combining these prime implicants covers all minterms, resulting in the simplified expression $F = y' + w'z' + xz'$.