An old-timey brute force way to do it is to simultaneously load the output of your full adder (after the addition is done) into a binary down-counter and clear a decade up- counter.

Then, using the same clock to run both counters, proceed until the down counter gets to zero, at which point the decade counter's contents will be the BCD equivalent of the binary full-adder's output.



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Will it work for an 8-bit input to 10-bit BCD output (2 bits for hundreds since it can only go up to 2) by connecting one more BCD counter?

 

Will it work for an 8-bit input to 10-bit BCD output (2 bits for hundreds since it can only go up to 2) by connecting one more BCD counter?

Yes, it will work for any number of digits just by increasing then number of counters.