Question

E) show algebraic expression for f in SOP (Sum of Product) form and pOS form (product of sum) (2. Marks) f(X,Y,Z)−Σm(1,2,5,6,7)

d) Using switching algebra properties, reduce the following expression to a minimum SOP form: (2 Marks) r=A′B′X′ + A′B′C′ + A′B′C
e) Using switching algebra properties, foduce the following expression to a mininum POS form: f=(A+B+C)(A+B+C′)(A+B′+C′) (2 Marks)

Answer 1

The algebraic expression for f in SOP form is (X' + Y' + Z) * (X' + Y + Z) * (X + Y + Z') * (X + Y + Z), and in POS form it is (X + Y + Z) + (X' + Y + Z') + (X' + Y' + Z').

Step-by-step explanation:

In SOP (Sum of Product) form, the algebraic expression for f would be:

f = (X' + Y' + Z) * (X' + Y + Z) * (X + Y + Z') * (X + Y + Z)

In POS (Product of Sum) form, the algebraic expression for f would be:

f = (X + Y + Z) + (X' + Y + Z') + (X' + Y' + Z')

To represent the function f(X, Y, Z) given by minterms 1, 2, 5, 6, and 7, in SOP (Sum of Product) and POS (Product of Sum) forms, we construct each form based on these individual minterms.

Next, for the expression r in SOP form and the expression f in POS form, we must apply switching algebra properties to reduce them to their simplest forms by eliminating terms wherever possible and ensuring that the simplifications are reasonable.

This will yield us the most simplified algebraic expressions in both SOP and POS forms.