Zero One is the Bynar partner of One Zero, part of the team that secretly modifies the Enterprise-D at Starbase 74 and takes it to Bynaus.
Zero One appears in 11001001. Like all Bynars, Zero One is linked to a partner and to the planetary computer of Bynaus, speaking in rapid bursts of binary sound when conferring and finishing the other's sentences when talking to outsiders.
With One Zero and a second pair, Zero One works on the Enterprise-D's systems at Starbase 74. The crew find them unusually nervous. Their real aim is to borrow the largest mobile computer in reach, since an electromagnetic pulse from a dying star threatens to wipe the system on which their society depends.
After the ship is recovered and Bynaus restored, the Bynars accept that they will have to answer for the theft. Picard acknowledges that they may well have been right to doubt they would be given the ship.