arithmetic – For the implementation in addition to a BCD figure, are these ways correct?

I have two ways to implement the 9's complement of the BCD number.

The first way I tried is the following:
Right here
What I did was that if we have 4 bits T like abcd:

1001 (~ 9) - abcd (in BCD) = 1001 + (complement to 2 of abcd) = complement to 9

the picture a diagram implementation.

The next way is as below:
Right here
in which I showed a truth table of 4 digits of T bits (BCD abcd) in input and a complement of 9 in T output, and then using K-map I, I also have the circuit.

My question is whether these means are correct for the complement of 9 or not.