Question

from the following k - map, we could write the function f (without simplification) as: f=xyz+xyz+xyz+xyzw ○ f=xyzw+xyzw ○ f=xyz+xyz+xyz+xyzw+xyzw ○ f=xyz+xyz+xyz ○ there is no right answer ○

Explanation:

Step1: Recall k - map to Boolean conversion

For a 4 - variable k - map with variables \(x,y,z,w\), each cell corresponds to a min - term. A 1 in a cell means the corresponding min - term is included in the sum - of - products (SOP) form of the function.

Step2: Identify min - terms for 1s in the k - map

• For the cell with \(x = 0,y=0,z = 1\) (first row, second column), the min - term is \(x'y'z\).
• For the cell with \(x = 1,y = 1,z=1\) (third row, second column), the min - term is \(xyz\).
• For the cell with \(x = 1,y = 1,z = 0\) (third row, first column), the min - term is \(xyz'\).
• For the cell with \(x = 1,y = 0,z = 1,w\) (second row, second column with \(w\) involved) the min - term is \(xy'zw\).
• For the cell with \(x = 0,y = 1,z = 0,w\) (second row, first column with \(w\) involved) the min - term is \(x'yz'w\).

Step3: Write the SOP function

The function \(f\) in sum - of - products form is \(f=x'y'z + xyz+xyz'+xy'zw+x'yz'w\)

Answer:

\(f=x'y'z + xyz+xyz'+xy'zw+x'yz'w\) (corresponding to the third option in the given multiple - choice)