Consider the circuit in below figure which has a four bit binary number $b_3b_2b_1b_0$ as input and a five bit binary number, $d_4d_3d_2d_1d_0$ as output.

Note that the last $4$ combinations ($1100$, $1101$, $1110$, $1111$) leads to $b_{3}$ and $b_2$ as $1$. So, in these combinations only $0100$ will be added.

$1100$ is $12$
$1101$ is $13$
$1110$ is $14$
$1111$ is $15$
in binary unsigned number system.

$1100 + 0100 = 10000$.
$1101 + 0100 = 10001$ and so on.
This is conversion to radix $12$.

$d_3d_2d_1d_0$ represents the $4$ bit binary equivalent of least significant digit of $radix \ 12$ and $d_4$ represent most significant digit of $radix \ 12.$