Question:
The simultaneous equations on the Boolean variables x, y, z, and w are: x + y + z = 1, xy = 0, x + y + w = 1, xy + z = 0. The solution for x, y, z, and w, respectively, is:
The simultaneous equations on the Boolean variables x, y, z, and w are: x + y + z = 1, xy = 0, x + y + w = 1, xy + z = 0. The solution for x, y, z, and w, respectively, is:
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Translate Boolean equations into logical constraints to systematically solve for each variable.
Updated On: Dec 29, 2024
- 0100
- 1011
- 1000
- 1101
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The Correct Option is A
Solution and Explanation
From the given equations: 1. x + y + z = 1: At least one of x, y, z is 1. 2. xy = 0: At least one of x or y is 0. 3. x + y + w = 1: At least one of x, y, w is 1. 4. xy + z = 0: z must be 1 because xy = 0. Solving these equations gives x = 0, y = 1, z = 0, w = 0. Thus, the solution is 0100.
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