Question

Given the following Karnaugh Map for a Boolean function \( F(w,x,y,z) \): 

Which one or more of the following Boolean expression(s) represent(s) \( F \)?

• A. \(\bar{w} \bar{x} \bar{y} z + w \bar{x} \bar{y} z + w \bar{x} y z + w \bar{x} \bar{y} \bar{z} + xz\)
• B. \(\bar{w} \bar{x} \bar{y} z + w \bar{x} \bar{y} z + w \bar{x} y z + xz\)
• C. \(\bar{w} \bar{x} \bar{y} z + w \bar{x} \bar{y} z + w \bar{x} y z\)
• D. \( xz + \bar{x}z \)

Hint:

{When simplifying Boolean expressions, always check for missing minterms by verifying the Karnaugh Map grouping.}

Answer 1

The Correct Option is A, D

- The Karnaugh Map groups the 1s into minimal sum-of-products expressions, which helps in simplifying complex Boolean functions.

- The correct sum-of-products expressions are derived by carefully grouping the 1s in the Karnaugh Map. This simplification process leads to the correct expressions found in options (A) and (D).

- Options (B) and (C) are incorrect because they are missing essential terms and do not fully represent \( F(w,x,y,z) \), which makes them incomplete expressions.

Thus, the correct options are (A) and (D).