Question 7.13: The truth table for three variable inputs and single output ...
The truth table for three variable inputs and single output logic circuit is shown below. Note that for three inputs the combinations are 2^{3} = 8. Construct the logic circuit using AND and OR gates
| A | B | C | X |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |
From observing the truth table we find that output is high, i.e., 1 for the inputs at rows 1, 3, and 6. Inputs at A, B, and C is 1 and complement A, \overline{B} \overline{n} is 0.
By writing the sum of all terms for which the output attains a high
Using the above Boolean expression, the logic circuit is drawn as in Fig. 7.12.
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