i) consider the first range of i\p voltage as $o\lt V_{A} \lt v_{R}/4$. In this range the ref. voltage $v_{1}, v_{2} and v_{3}$ are all higher than the I/p voltage . The o/p voltage of all the comparators are low I.e $c_{1},c_{2}, c_{3}$= 000 the corresponding o/p of the priority encoder is 00

ii) in the second range $v_R/{4} \lt v_{A}\lt v_{R/2}$ the ref voltages $v_{1}=v_{R/4}$ is less than $v_{A}$. The o/p of comparator 1 is only high $c_{1} c_{2} c_{3}$=100 . The o/p of the priority encoder is 01

The comparators o/p for the various windows and the priority encoder o/p are given as