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Given the following Karnaugh Map for a Boolean function F(w,x,y,z):
The 4×4 K-map has rows labeled by wx and columns labeled by yz, with cell values:
Row 1: 1 0 0 1
Row 2: 0 1 1 0
Row 3: 0 1 1 0
Row 4: 1 0 0 1
Which one or more of the following Boolean expression(s) represent(s) F?
- w̅x̅y̅z̅ + wx̅y̅z̅ + w̅xy̅z̅ + wx̅yz̅ + xz
- w̅x̅y̅z̅ + w̅xy̅z̅ + wx̅yz + xz
- wx̅y̅z̅ + wx̅yz̅ + w̅x̅y̅z̅ + xz
- x̅z̅ + xz
Correct answer: x̅z̅ + xz
Solution
The expression x̅z̅ + xz simplifies to cover the cases where z is either 0 or 1, regardless of the value of x, which matches the output of the K-map. This indicates that the function F is true for both conditions of x when z is fixed, making it the correct representation.
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