Priority Encoder Design

A Priority Encoder is a combinational circuit that takes a bit vector as input and outputs the binary number corresponding to the position of the highest$-$priority active bit. For example, when a $4-$bit vector $(\{$I$3,$I$2,$I$1,$I$0\}=0011)$ is input, and assuming that the most significant bit $($MSB$)$ has the highest priority, the circuit will output the position of the highest priority bit $($in this case, the $1$st bit$)$ as a binary number $1(\{$O$1,$O$0\}=01)$

In the given block diagram, write the Boolean expressions for D$0,$ D$1,$ D$2,$ and D$3.($A Binary Encoder is the opposite of a Binary Decoder. In a Binary Encoder, one bit in the input vector is always set to $1,$ and the encoder outputs the binary number corresponding to the position of that bit. For example, in the circuit shown below, if $)(\{$D$3,$ D$2,$ D$1,$ D$0\}=0100),$ the output will be $(\{$O$1$O$0\}=10)$