Question

What is the Boolean expression for the output f of the combinational logic circuit of NAND gates given below:

• A. $\overline{Q}+\overline{R}$
• B. $\overline{Q}\overline{R}$
• C. $\overline{P}+\overline{R}$
• D. $\overline{Q}\overline{R}\overline{R}$

Answer 1

The correct option is A $\overline{Q}+\overline{R}$

$F=(\overline{PQ+R)-(PR+QR)}$

$F=\overline{PQR+PQR+PQR+QR}$

$F=\overline{PQR+QR}$

$F=\overline{(P+1)QR}=\overline{QR}$

$F=\overline{Q}+\overline{R}$