Question

A combinational logic circuit with three inputs P, Q, R produces output 1 if and only if an odd number of 0’s are inputs.

(i) Draw its truth table. 

(ii) Derive a canonical SOP expression for the above truth table. 

(iii) Find the complement of the above-derived expression using De Morgan’s theorem and verify if it is equivalent to its POS expression.

Answer 1

(i)

(ii) X (P, Q, R) = P’Q’R’ + P’QR + PQ’R + PQR’ 

(iii) Complement of X (P, Q, R) = (P + Q + R). (P + Q’ + R’). (P’ + Q + R’). (P’ + Q’ + R) which is not equal to POS expression for the above Truth Table.