Question

Let the Boolean function be f(a,b,c)= ⅀ m(0,4,5,7), represent the min-terms of f(a,b,c) and let f(a,b,c)=ℿ M(1,2,3,6), represent the maxterms of f(a,b,c)

Obtain minimal POS and SOP for f(a,b,c)

Answer 1

The minimal Product of Sums (POS) and Sum of Products (SOP) forms of the Boolean function are calculated by converting the given minterms and maxterms to disjunctions of conjunctions and conjunctions of disjunctions, respectively, based on the binary representations of the terms.

Step-by-step explanation:

To finding the minimal Product of Sums (POS) and Sum of Products (SOP) forms of a Boolean function given in the standard minterm and maxterm notations. The minterms are represented by f(a,b,c) = ∑ m(0,4,5,7), which means that the function takes the value 1 for the binary combinations of a, b, and c that correspond to the decimal numbers 0, 4, 5, and 7. The maxterms are given by f(a,b,c) = ℝ M(1,2,3,6), indicating that the function takes the value 0 for the combinations corresponding to the decimal numbers 1, 2, 3, and 6.

To obtain the minimal SOP form, we write the minterms as the disjunction (OR) of conjunctions (AND) of the variables or their complements, based on the binary representation of the minterms. Similarly, to get the minimal POS form, we consider the maxterms and write the conjuction (AND) of disjunctions (OR) of the variables or their complements based on the binary representation of the maxterms.

Minimal SOP for f(a,b,c) = a'b'c' + a'bc + ab'c + abc
Minimal POS for f(a,b,c) = (a + b + c)(a + b' + c')(a' + b + c)(a' + b' + c')