Simplified Boolean equation for the following truth table is :…
2016
Simplified Boolean equation for the following truth table is :
\(\begin{array}{|c|c|c|c|}\hline x & y & z & F \\ \hline \text{0} & \text{0} & \text{0} & \text{0} \\ \hline \text{0} & \text{0} & \text{1} & \text{1} \\ \hline \text{0} & \text{1} & \text{0} & \text{0} \\ \hline \text{0} & \text{1} & \text{1} & \text{1} \\ \hline \text{1} & \text{0} & \text{0} & \text{1} \\ \hline \text{1} & \text{0} & \text{1} & \text{0} \\ \hline \text{1} & \text{1} & \text{0} & \text{1} \\ \hline \text{1} & \text{1} & \text{1} & \text{0} \\ \hline \end{array}\)
- A.
\(F=y \bar{z}+\bar{y}z\) - B.
\(F=x \bar{y}+\bar{x}y\) - C.
\(F=\bar{x}z+x\bar{z}\) - D.
\(F=\bar{x}z+x\bar{z}+xyz\)
Attempted by 107 students.
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Correct answer: C
Minterms where F = 1: (0,0,1), (0,1,1), (1,0,0), (1,1,0)
Combine terms with the same z value:
For z = 1: combine (0,0,1) and (0,1,1) to get x' z.
For z = 0: combine (1,0,0) and (1,1,0) to get x z'.
Final simplified expression: F = x' z + x z' = x XOR z (independent of y).