Thank you in advance!

I am wiring up a 110V outlet to go on the side of my table saw outfeed
extension table recently built.
I would like to tap this off of the 220V outlet for the table saw, directly
beneath the new bench.
I know I can get 110 from this by putting the black wire on one of the 220V
outlets hot post and the
white wire on the neutral ...now...should the green wire (in the cord going
to the new outlet) also
go to the same post as the white / neutral since both are at ground
potential?

Steve