The simultaneous equations on the Boolean variables x, y, z and w are: x + y +…

2000

The simultaneous equations on the Boolean variables x, y, z and w are:

x + y + z = 1
xy = 0
xz + w = 1
xy + z'w' = 0

They have the following solution for x, y, z and w, respectively.

  1. A.

    0 1 0 0

  2. B.

    1 1 0 1

  3. C.

    1 0 1 1

  4. D.

    1 0 0 0

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Correct answer: C

Check the options by substitution in the given Boolean equations.

For x = 1, y = 0, z = 1, w = 1:
x + y + z = 1 + 0 + 1 = 1,
xy = 1·0 = 0,
xz + w = 1·1 + 1 = 1,
xy + z'w' = 1·0 + 0·0 = 0.

All four equations are satisfied. The other options fail at least one equation. Therefore, the solution is x = 1, y = 0, z = 1, w = 1.

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