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Question
Give the truth table for Z = x(y + xz + x')
Short Answer
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Solution
Simplification:
[Z = xy + xxz + xx']
[Z = xy + xz + 0]
[Z = x(y + z)]
| x | y | z | Z |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Thus, [Z = 1] only when [x = 1] and at least one of [y] or [z] is 1.
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