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Question
From the truth table below, determine SOP and POS expression.
| A | B | C | Output X |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 |
Long Answer
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Solution
From the truth table:
Output X = 1 for:
001, 011, 110
SOP Expression
X = A′B′C + A′BC + ABC′
X = Σm(1, 3, 6)
Simplified SOP:
X = A′C + ABC′
POS Expression
Output X = 0 for:
000, 010, 100, 101, 111
Therefore,
X = (A + B + C)(A + B′ + C)(A′ + B + C)(A′ + B + C′)(A′ + B′ + C′)
X = ΠM(0, 2, 4, 5, 7)
Simplified POS:
X = (A + C)(A′ + B)(A′ + C′)
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