Question

YZ+XY' to canonical sum of product​

Answer 1

Answer:

Given expression: F(x,y,z) = YZ + XY'

The number of variables for the above expression is 3. (x,y and z)

Since the given form is of minimal Sum of Products form, we are required to find the Canonical Sum of products.

Step 1: Calculating the missing variables in each term.

First term: YZ

Missing Variable: X

Second Term: XY'

Missing Variable: Z

Step 2: Rewriting the missing variable by adding 1 using the AND operator. That is,

First Term after adding missing term: 1.Y.Z

Second Term after adding the missing term: X.Y'.1

Now according to Boolean Algebra,

⇒ ( X + X' ) = 1

Hence substituting the value of 1 in terms of missing variable we get:

⇒ First Term = ( X + X' ).Y.Z

⇒ First Term = X.Y.Z + X'.Y.Z   ...(i)

⇒ Second Term = X.Y'.( Z + Z')

⇒ Second Term = X.Y'.Z + X.Y'.Z'   ...(ii)

Combining (i) and (ii) using AND operator we get:

⇒ F(x,y,z) = X.Y.Z + X'.Y.Z + X.Y'.Z + X.Y'.Z'

Converting the terms from binary to decimal values we get:

• X.Y.Z = 111 = 7
• X'.Y.Z = 011 = 3
• X.Y'.Z = 101 = 5
• X.Y'.Z' = 100 = 4

Hence in terms of minterms we can represent it as:

⇒ F(x,y,z) = ∑ m(3,4,5,7)