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Express F in SOP and POS form
written 5.4 years ago by | modified 4.5 years ago by |
With its truth table, express F in SOP and POS form $$F(A,B,C) = \sum m(0,3,5,7)$$
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written 5.4 years ago by | modified 4.5 years ago by |
With its truth table, express F in SOP and POS form $$F(A,B,C) = \sum m(0,3,5,7)$$
written 5.4 years ago by |
Since, there are 3 variables - A, B, C, so the number of select lines = 3.
Therefore, number of data inputs = $2^3=8$
Therefore, 8:1 MUX is needed.
Sum of Product (SOP)
For SOP, connect all the minterm inputs i.e 0,3,5,7 to logic 1 and rest of the input lines to logic 0.
The truth table is as shown -
Input Line | A | B | C | Output F |
---|---|---|---|---|
0 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
2 | 0 | 1 | 0 | 0 |
3 | 0 | 1 | 1 | 1 |
4 | 1 | 0 | 0 | 0 |
5 | 1 | 0 | 1 | 1 |
6 | 1 | 1 | 0 | 0 |
7 | 1 | 1 | 1 | 1 |
Product of Sum (POS)
For POS, connect all the maxterm inputs i.e 0,3,5,7 to logic 0 and rest of the input lines to logic 1.
The truth table is as shown -
Input Line | A | B | C | Output F |
---|---|---|---|---|
0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 |
2 | 0 | 1 | 0 | 1 |
3 | 0 | 1 | 1 | 0 |
4 | 1 | 0 | 0 | 1 |
5 | 1 | 0 | 1 | 0 |
6 | 1 | 1 | 0 | 1 |
7 | 1 | 1 | 1 | 0 |