Question

Develop sum of products and product of sums expressions for F₁ and F₂ from the following truth table :

Answer 1

Add a new column containing Minterms. Now the table is as follows :

Now by adding all the minterms for which output is 1 in F1, we get desired sum-of-products expression which is X’YZ’ + X’YZ + XY’Z’ + XYZ

Now by adding all the minterms for which output is 1 in F2, we get desired sum-of-products expression which is X’Y’Z + X’YZ’ + XYZ’ + XYZ

Now by multiplying Maxterms for the output 0s in F1, we get the desired product of sums expression which is (X + Y + Z)( X + Y + Z’)( X’ + Y + Z’)( X’ + Y ‘+ Z)

Now by multiplying Maxterms for the output 0s in F2, we get the desired product of sums expression which is (X + Y + Z)( X + Y’ + Z’)( X’ + Y + Z)( X’ + Y + Z’)