Obtaining the logic function from the truth table: Shannon Theorem
Combinational logic circuits are solved taking as input the truth table, since this establishes all the possible input and output combinations. Taking as input the truth table, we can establish a logic function in two possible forms:
(1) First canonical form or disjunctive canonical form (sum of product or minterms)
(2) Second canonical form or conjunctive canonical form (product of sums or maxterms).
In the first canonical form, SoP (Sum of Products) is obtained by adding all the minterms that give 1 as output. In a minterm 0 is assigned to the inversed variable and 1 to the direct variable (Shannon Theorem).
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First canonical form |
Second canonical form |
The second canonical form, PoS (Product of Sums), is obtained in a dual form to the previous one: by multiplying the maxiterms whose result column is 0. The maxiterm is the miniterm dual.
Looking at the following example:
