Simplify the following Boolean expression using K$-$ Map and write the truth table

with the circuit diagram using only NOR gates.

$F\frac{?}{b}=ar\frac{B}{b}ar(C)+\frac{A}{b}ar(B)+A\frac{B}{b}ar(C)+\frac{A}{b}ar(B)\frac{C}{b}ar(D)\frac{+}{b}ar\frac{A}{b}ar\frac{B}{b}ar(C)D+\frac{A}{b}ar(B)CD$