I don't understand converting BCD to 4-bit binary. BCD
is 4-bit binary.
There is no easy way to convert BCD to binary. To convert 3 digits of BCD to one binary word requires a huge amount of logic if you are limited to using only logical gates. You would need to generate a truth table for all 999 states and then convert that to logic using Boolean algebra.
Using a adder would require first multiplying the second BCD word by ten and the third BCD word by 100 before you add them all together, and multiplying is a sequential process (shift and add), not a static one.