Consider the block diagram shown in Fig. $1.$ The input is a four bit binary number A $=$ a$3$a$2$a$1$a$0,$ where a$3$ as the most$-$significant bit $($MSB$).$a$)$ Give the truth table for a combinational circuit that encodes this number in two stages: the first stage converts A to Gray code G $=$ g$3$g$2$g$1$g$0,$ where g$3$ is the MSB$.$ The second stage encodes G to a two$-$bit binary code C $=$ c$1$c$0$ using a priority encoder. The priority order is g$3>$g$2>$g$1>$g$0$ bit indicating that one or more bits in the Gray code are equal to $1.$b$)$ Express the functions for the three outputs c$1,$ c$0,$ V $,$ in their SOP form in terms of ai$.$ For the case V $=0,1$ and c$0.$