Question

convert the following to canonical SOP F(X, Y, Z) =X.Y+Y'.Z+Z'​

Answer 1

for different Boolean functions. In this section, we will learn about how we can represent the POS form in the SOP form and SOP form in the POS form.

For converting the canonical expressions, we have to change the symbols ∏, ∑. These symbols are changed when we list out the index numbers of the equations. From the original form of the equation, these indices numbers are excluded. The SOP and POS forms of the boolean function are duals to each other.

There are the following steps using which we can easily convert the canonical forms of the equations:

Change the operational symbols used in the equation, such as ∑, ∏.

Use the Duality's De-Morgan's principal to write the indexes of the terms that are not presented in the given form of an equation or the index numbers of the Boolean function.

Conversion of POS to SOP form

For getting the SOP form from the POS form, we have to change the symbol ∏ to ∑. After that, we write the numeric indexes of missing variables of the given Boolean function.

There are the following steps to convert the POS function F = Π x, y, z (2, 3, 5) = x y' z' + x y' z + x y z' into SOP form:

In the first step, we change the operational sign to Σ.

Next, we find the missing indexes of the terms, 000, 110, 001, 100, and 111.

Finally, we write the product form of the noted terms.

000 = x' * y' * z'

001 = x' * y' * z

100 = x * y' * z'

110 = x * y* z'

111 = x * y * z

So the SOP form is:

F = Σ x, y, z (0, 1, 4, 6, 7) = (x' * y' * z') + (x' * y' * z) + (x * y' * z') + (x * y* z') + (x * y * z)