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Question
For the given truth table, write Boolean expression for function G1, G2, G3, G4, G5.
| X | Y | Z | G1 | G2 | G3 | G4 | G5 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
Short Answer
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Solution
Using the rows where each function is 1:
[G1 = X'YZ' + X'YZ + XY'Z' = X'Y + XY'Z']
[G2 = X'Y'Z + X'YZ + XYZ' = X'Z + XYZ']
[G3 = XY'Z + XYZ' + XYZ = XY'Z + XY]
[G4 = X'Y'Z + X'YZ' + X'YZ + XY'Z' = X'Y + XY'Z']
[G5 = X'Y'Z' + XY'Z' + XY'Z + XYZ]
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