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.
- A.
0 1 0 0
- B.
1 1 0 1
- C.
1 0 1 1
- 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.