One Zero is one of the paired Bynars who upgrade the Enterprise-D computer at Starbase 74 and then hijack the ship to save their homeworld's data.
One Zero appears in 11001001. Bynars live and work in linked pairs, and One Zero is partnered with Zero One. The two come aboard at Starbase 74 under Commander Quinteros to enhance the ship's computer and holodecks.
Joined by a second pair, they create the hologram Minuet to keep Riker and Picard occupied, fake a containment failure so the ship is evacuated, and then take it to Bynaus. A nearby star is about to go nova, and the planet's central computer must be shut down with its contents stored in the Enterprise's memory.
The pulse comes sooner than expected and the four Bynars collapse. Picard and Riker find the file and restore the data to Bynaus, reviving them. They explain that they stole the ship because they feared a request might be refused.