Implement the product-of-sums Boolean function expressed by Π1,2,5 by a suitable multiplexer.
Question 8.1: Implement the product-of-sums Boolean function expressed by ...
• Let the Boolean function be f\left(A,B,C\right) =\Pi 1,2,5
• The equivalent sum-of-products expression can be written as f\left(A,B,C\right) =\sum{0,3,4,6,7}
The truth table for the given Boolean function is given in Table 8.5. The given function can be implemented with a 4-to-1 multiplexer with two selection lines. Variables A and B are chosen for the selection lines. The implementation table as drawn with the help of the truth table is given in Table 8.6.
Figure 8.12 shows the hardware implementation.
| Table 8.5 Truth table. | |||
| f(A,B,C) | A | B | C |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
| Table 8.6 Implementation table. | ||||
| I_{3} | I_{2} | I_{1} | I_{0} | |
| 3 | 2 | 1 | 0 | \overline{C} |
| 7 | 6 | 5 | 4 | C |
| 1 | C | 0 | 1 | |
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