# Sum-of-Product understanding

I am trying to learn Sum-of-Products and minterms and maxterms for logic design, but I don't know how the book gets the f(x1,x2,x3) part.

I think I understand the minterm from the first pic (it's like you do the inversion if any of the bit is 0?), but the part I dont get is the second picture where from x1,x2,and x3, they get the f(x1,x2,x3).

How did they get from the row numbers to f(x1,x2,x3)?

I dont get is the second picture where from x1,x2,and x3, they get the f(x1,x2,x3).

In the second table, the given f(x1, x2, x3) is part of the problem statement.

For any f(x1, x2, x3) function you are given, you can find a SOP representation, and from there design the logic to implement the function.

The one in the table is just an example to illustrate this procedure.

The first Table represents how each of the $$\f(x_1, x_2, x_3)\$$ are represented as minterms and maxterms.

Minterms are 1, so if the truth table is 1, that term is a part of the solution. Maxterms 0, so a 0 in the truth table, means that term is a part of the solution.

If 000 = 1, then $$\ \overline {x_1}\cdot \overline {x_2}\cdot \overline {x_3}\$$ is a part of the minterm solution f.

Otherwise if 000 = 0, $$\ x_1 + x_2 + x_3\$$ is a part of the maxterm solution f.

Both minterm and maxterms solutions are equivalent.

The second Table is where you get to apply Table 1. Solve both and then minimize both and you will get the same answer.